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?
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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?
$begingroup$
I have come across the topological space $mathbbR^mathbbR$, but I would like to know exactly what it is.
- Is it a space of all real-valued functions of a real variable?
- Is it a product space of $mathbbR$ raised to a power of $mathbbR$?
Any help will be greatly appreciated.
general-topology
asked Mar 27 at 18:01
JamesJames
30818
$endgroup$
add a comment |
$begingroup$
I have come across the topological space $mathbbR^mathbbR$, but I would like to know exactly what it is.
- Is it a space of all real-valued functions of a real variable?
- Is it a product space of $mathbbR$ raised to a power of $mathbbR$?
Any help will be greatly appreciated.
general-topology
asked Mar 27 at 18:01
JamesJames
30818
$endgroup$
$begingroup$
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
add a comment |
$begingroup$
I have come across the topological space $mathbbR^mathbbR$, but I would like to know exactly what it is.
- Is it a space of all real-valued functions of a real variable?
- Is it a product space of $mathbbR$ raised to a power of $mathbbR$?
Any help will be greatly appreciated.
general-topology
asked Mar 27 at 18:01
JamesJames
30818
$endgroup$
I have come across the topological space $mathbbR^mathbbR$, but I would like to know exactly what it is.
- Is it a space of all real-valued functions of a real variable?
- Is it a product space of $mathbbR$ raised to a power of $mathbbR$?
Any help will be greatly appreciated.
general-topology
general-topology
asked Mar 27 at 18:01
JamesJames
30818
asked Mar 27 at 18:01
JamesJames
30818
asked Mar 27 at 18:01
JamesJames
30818
asked Mar 27 at 18:01
JamesJames
30818
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
add a comment |
$begingroup$
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
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
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. $v_a = f(a)$.
answered Mar 27 at 18:08
Robert IsraelRobert Israel
332k23222481
$endgroup$
$begingroup$
Thank you so much for making things clearer, now I understand it.
$endgroup$
– James
Mar 28 at 16:29
add a comment |
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1 Answer
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active
oldest
votes
1 Answer
1
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oldest
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$begingroup$
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. $v_a = f(a)$.
answered Mar 27 at 18:08
Robert IsraelRobert Israel
332k23222481
$endgroup$
$begingroup$
Thank you so much for making things clearer, now I understand it.
$endgroup$
– James
Mar 28 at 16:29
add a comment |
$begingroup$
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. $v_a = f(a)$.
answered Mar 27 at 18:08
Robert IsraelRobert Israel
332k23222481
$endgroup$
$begingroup$
Thank you so much for making things clearer, now I understand it.
$endgroup$
– James
Mar 28 at 16:29
add a comment |
$begingroup$
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. $v_a = f(a)$.
answered Mar 27 at 18:08
Robert IsraelRobert Israel
332k23222481
$endgroup$
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. $v_a = f(a)$.
answered Mar 27 at 18:08
Robert IsraelRobert Israel
332k23222481
answered Mar 27 at 18:08
Robert IsraelRobert Israel
332k23222481
answered Mar 27 at 18:08
Robert IsraelRobert Israel
332k23222481
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
add a comment |
$begingroup$
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
add a comment |
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$begingroup$
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