What exactly is the topological space $mathbbR^mathbbR$? Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 23, 2019 at 00:00UTC (8:00pm US/Eastern)Topology: Continuous FunctionsEmbedding $mathbbQ$ with the usual topology into a power of the two point discrete space?What topological group is $mathbb R/mathbb Z$?What does it mean for a topological space to contain a copy of $mathbbR$?What is the dual category of topological spaces?Is whether every topological space the continuous image of a metric space?Set of boundaries in topological spaceWhat is more general than a topological space?Aren't all sets in a topological space open??What is the usefulness of a separable space in topology, especially in terms of real-valued functions on the space?

Multi tool use
Multi tool use

Why does the remaining Rebel fleet at the end of Rogue One seem dramatically larger than the one in A New Hope?

Project Euler #1 in C++

How do I find out the mythology and history of my Fortress?

Why wasn't DOSKEY integrated with COMMAND.COM?

Why is it faster to reheat something than it is to cook it?

Why weren't discrete x86 CPUs ever used in game hardware?

How could we fake a moon landing now?

ArcGIS Pro Python arcpy.CreatePersonalGDB_management

How come Sam didn't become Lord of Horn Hill?

What initially awakened the Balrog?

A term for a woman complaining about things/begging in a cute/childish way

Hangman Game with C++

How does light 'choose' between wave and particle behaviour?

How do living politicians protect their readily obtainable signatures from misuse?

What do you call the main part of a joke?

How do I change colors in Zim (wiki editor) running on Kubuntu 18.10?

How would a mousetrap for use in space work?

What is this clumpy 20-30cm high yellow-flowered plant?

How does the math work when buying airline miles?

Why should I vote and accept answers?

Illegal assignment from sObject to Id

Sum letters are not two different

What would you call this weird metallic apparatus that allows you to lift people?

Is it fair for a professor to grade us on the possession of past papers?



What exactly is the topological space $mathbbR^mathbbR$?



Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 23, 2019 at 00:00UTC (8:00pm US/Eastern)Topology: Continuous FunctionsEmbedding $mathbbQ$ with the usual topology into a power of the two point discrete space?What topological group is $mathbb R/mathbb Z$?What does it mean for a topological space to contain a copy of $mathbbR$?What is the dual category of topological spaces?Is whether every topological space the continuous image of a metric space?Set of boundaries in topological spaceWhat is more general than a topological space?Aren't all sets in a topological space open??What is the usefulness of a separable space in topology, especially in terms of real-valued functions on the space?










1












$begingroup$


I have come across the topological space $mathbbR^mathbbR$, but I would like to know exactly what it is.



  1. Is it a space of all real-valued functions of a real variable?

  2. Is it a product space of $mathbbR$ raised to a power of $mathbbR$?

Any help will be greatly appreciated.










share|cite|improve this question









$endgroup$











  • $begingroup$
    I think the definition may depend upon the source you are using.
    $endgroup$
    – Mann
    Mar 27 at 18:04










  • $begingroup$
    Remember that $A^B$ is often notation for the set of functions from $B$ to $A$
    $endgroup$
    – Don Thousand
    Mar 27 at 18:04
















1












$begingroup$


I have come across the topological space $mathbbR^mathbbR$, but I would like to know exactly what it is.



  1. Is it a space of all real-valued functions of a real variable?

  2. Is it a product space of $mathbbR$ raised to a power of $mathbbR$?

Any help will be greatly appreciated.










share|cite|improve this question









$endgroup$











  • $begingroup$
    I think the definition may depend upon the source you are using.
    $endgroup$
    – Mann
    Mar 27 at 18:04










  • $begingroup$
    Remember that $A^B$ is often notation for the set of functions from $B$ to $A$
    $endgroup$
    – Don Thousand
    Mar 27 at 18:04














1












1








1





$begingroup$


I have come across the topological space $mathbbR^mathbbR$, but I would like to know exactly what it is.



  1. Is it a space of all real-valued functions of a real variable?

  2. Is it a product space of $mathbbR$ raised to a power of $mathbbR$?

Any help will be greatly appreciated.










share|cite|improve this question









$endgroup$




I have come across the topological space $mathbbR^mathbbR$, but I would like to know exactly what it is.



  1. Is it a space of all real-valued functions of a real variable?

  2. Is it a product space of $mathbbR$ raised to a power of $mathbbR$?

Any help will be greatly appreciated.







general-topology






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Mar 27 at 18:01









JamesJames

30818




30818











  • $begingroup$
    I think the definition may depend upon the source you are using.
    $endgroup$
    – Mann
    Mar 27 at 18:04










  • $begingroup$
    Remember that $A^B$ is often notation for the set of functions from $B$ to $A$
    $endgroup$
    – Don Thousand
    Mar 27 at 18:04

















  • $begingroup$
    I think the definition may depend upon the source you are using.
    $endgroup$
    – Mann
    Mar 27 at 18:04










  • $begingroup$
    Remember that $A^B$ is often notation for the set of functions from $B$ to $A$
    $endgroup$
    – Don Thousand
    Mar 27 at 18:04
















$begingroup$
I think the definition may depend upon the source you are using.
$endgroup$
– Mann
Mar 27 at 18:04




$begingroup$
I think the definition may depend upon the source you are using.
$endgroup$
– Mann
Mar 27 at 18:04












$begingroup$
Remember that $A^B$ is often notation for the set of functions from $B$ to $A$
$endgroup$
– Don Thousand
Mar 27 at 18:04





$begingroup$
Remember that $A^B$ is often notation for the set of functions from $B$ to $A$
$endgroup$
– Don Thousand
Mar 27 at 18:04











1 Answer
1






active

oldest

votes


















7












$begingroup$

It is both. A function $f: A to B$ assigns a member of $B$ to each member of $A$. It can be thought of as a "tuple" $v in B^A$ indexed by the members of $A$, where each element of the tuple is a member of $B$, i.e. $v_a = f(a)$.






share|cite|improve this answer









$endgroup$












  • $begingroup$
    Thank you so much for making things clearer, now I understand it.
    $endgroup$
    – James
    Mar 28 at 16:29











Your Answer








StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);

else
createEditor();

);

function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);



);













draft saved

draft discarded


















StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3164871%2fwhat-exactly-is-the-topological-space-mathbbr-mathbbr%23new-answer', 'question_page');

);

Post as a guest















Required, but never shown

























1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









7












$begingroup$

It is both. A function $f: A to B$ assigns a member of $B$ to each member of $A$. It can be thought of as a "tuple" $v in B^A$ indexed by the members of $A$, where each element of the tuple is a member of $B$, i.e. $v_a = f(a)$.






share|cite|improve this answer









$endgroup$












  • $begingroup$
    Thank you so much for making things clearer, now I understand it.
    $endgroup$
    – James
    Mar 28 at 16:29















7












$begingroup$

It is both. A function $f: A to B$ assigns a member of $B$ to each member of $A$. It can be thought of as a "tuple" $v in B^A$ indexed by the members of $A$, where each element of the tuple is a member of $B$, i.e. $v_a = f(a)$.






share|cite|improve this answer









$endgroup$












  • $begingroup$
    Thank you so much for making things clearer, now I understand it.
    $endgroup$
    – James
    Mar 28 at 16:29













7












7








7





$begingroup$

It is both. A function $f: A to B$ assigns a member of $B$ to each member of $A$. It can be thought of as a "tuple" $v in B^A$ indexed by the members of $A$, where each element of the tuple is a member of $B$, i.e. $v_a = f(a)$.






share|cite|improve this answer









$endgroup$



It is both. A function $f: A to B$ assigns a member of $B$ to each member of $A$. It can be thought of as a "tuple" $v in B^A$ indexed by the members of $A$, where each element of the tuple is a member of $B$, i.e. $v_a = f(a)$.







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Mar 27 at 18:08









Robert IsraelRobert Israel

332k23222481




332k23222481











  • $begingroup$
    Thank you so much for making things clearer, now I understand it.
    $endgroup$
    – James
    Mar 28 at 16:29
















  • $begingroup$
    Thank you so much for making things clearer, now I understand it.
    $endgroup$
    – James
    Mar 28 at 16:29















$begingroup$
Thank you so much for making things clearer, now I understand it.
$endgroup$
– James
Mar 28 at 16:29




$begingroup$
Thank you so much for making things clearer, now I understand it.
$endgroup$
– James
Mar 28 at 16:29

















draft saved

draft discarded
















































Thanks for contributing an answer to Mathematics Stack Exchange!


  • Please be sure to answer the question. Provide details and share your research!

But avoid


  • Asking for help, clarification, or responding to other answers.

  • Making statements based on opinion; back them up with references or personal experience.

Use MathJax to format equations. MathJax reference.


To learn more, see our tips on writing great answers.




draft saved


draft discarded














StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3164871%2fwhat-exactly-is-the-topological-space-mathbbr-mathbbr%23new-answer', 'question_page');

);

Post as a guest















Required, but never shown





















































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown

































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown







ptgT4OufD6wpeolG v Nx79pUK,nx yAoBD 1opQbNzsOHuzQ W879R,qa,Dp2O87C vvpuyad
qSjyE6sOf MW,XpJ,vK2,gwb RojVd AE78M,K8SnKgUYtyAgzNW2

Popular posts from this blog

Football at the 1986 Brunei Merdeka Games Contents Teams Group stage Knockout stage References Navigation menu"Brunei Merdeka Games 1986".

Solar Wings Breeze Design and development Specifications (Breeze) References Navigation menu1368-485X"Hang glider: Breeze (Solar Wings)"e

Kathakali Contents Etymology and nomenclature History Repertoire Songs and musical instruments Traditional plays Styles: Sampradayam Training centers and awards Relationship to other dance forms See also Notes References External links Navigation menueThe Illustrated Encyclopedia of Hinduism: A-MSouth Asian Folklore: An EncyclopediaRoutledge International Encyclopedia of Women: Global Women's Issues and KnowledgeKathakali Dance-drama: Where Gods and Demons Come to PlayKathakali Dance-drama: Where Gods and Demons Come to PlayKathakali Dance-drama: Where Gods and Demons Come to Play10.1353/atj.2005.0004The Illustrated Encyclopedia of Hinduism: A-MEncyclopedia of HinduismKathakali Dance-drama: Where Gods and Demons Come to PlaySonic Liturgy: Ritual and Music in Hindu Tradition"The Mirror of Gesture"Kathakali Dance-drama: Where Gods and Demons Come to Play"Kathakali"Indian Theatre: Traditions of PerformanceIndian Theatre: Traditions of PerformanceIndian Theatre: Traditions of PerformanceIndian Theatre: Traditions of PerformanceMedieval Indian Literature: An AnthologyThe Oxford Companion to Indian TheatreSouth Asian Folklore: An Encyclopedia : Afghanistan, Bangladesh, India, Nepal, Pakistan, Sri LankaThe Rise of Performance Studies: Rethinking Richard Schechner's Broad SpectrumIndian Theatre: Traditions of PerformanceModern Asian Theatre and Performance 1900-2000Critical Theory and PerformanceBetween Theater and AnthropologyKathakali603847011Indian Theatre: Traditions of PerformanceIndian Theatre: Traditions of PerformanceIndian Theatre: Traditions of PerformanceBetween Theater and AnthropologyBetween Theater and AnthropologyNambeesan Smaraka AwardsArchivedThe Cambridge Guide to TheatreRoutledge International Encyclopedia of Women: Global Women's Issues and KnowledgeThe Garland Encyclopedia of World Music: South Asia : the Indian subcontinentThe Ethos of Noh: Actors and Their Art10.2307/1145740By Means of Performance: Intercultural Studies of Theatre and Ritual10.1017/s204912550000100xReconceiving the Renaissance: A Critical ReaderPerformance TheoryListening to Theatre: The Aural Dimension of Beijing Opera10.2307/1146013Kathakali: The Art of the Non-WorldlyOn KathakaliKathakali, the dance theatreThe Kathakali Complex: Performance & StructureKathakali Dance-Drama: Where Gods and Demons Come to Play10.1093/obo/9780195399318-0071Drama and Ritual of Early Hinduism"In the Shadow of Hollywood Orientalism: Authentic East Indian Dancing"10.1080/08949460490274013Sanskrit Play Production in Ancient IndiaIndian Music: History and StructureBharata, the Nāṭyaśāstra233639306Table of Contents2238067286469807Dance In Indian Painting10.2307/32047833204783Kathakali Dance-Theatre: A Visual Narrative of Sacred Indian MimeIndian Classical Dance: The Renaissance and BeyondKathakali: an indigenous art-form of Keralaeee