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Question about neighborhood of diagonal of a topological space

What exactly is a neighborhood of the diagonal on a topological space?On the Compact Uniformization TheoremIs every $T_4$ topological space divisible?Neighborhood of diagonalNeighborhood in topological groupsNeighborhood of $Delta_X$ in $Xtimes X$Topological space, equivalent statements, net, closure, neighborhoodIn discrete topology, every neighborhood of $Delta_X$ is an entourage?For every closed neighborhood $Delta_Xsubset D$ , Is there an entourage $U$ with $Usubseteq D$?Let $N$ be neighborhood of diagonal of $X$ $Delta_X$. Is it true $int(N)neq emptyset$?

1

$begingroup$

Let $X$ be a topological space but it is not uniform space and $U$ be a neighborhood of diagonal $X$, $Delta_X$. Is there a neighborhood $D(neq Delta_X)$ of $Delta_X$
such that $Dcirc D subseteq U$?

general-topology uniform-spaces

share|cite|improve this question

asked Mar 14 at 17:15

user479859user479859

987

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  There are counterexamples. Look in good books on uniform spaces...
  $endgroup$
  – Henno Brandsma
  Mar 17 at 22:23
  

  
  
  
  

add a comment | 

1

$begingroup$

Let $X$ be a topological space but it is not uniform space and $U$ be a neighborhood of diagonal $X$, $Delta_X$. Is there a neighborhood $D(neq Delta_X)$ of $Delta_X$
such that $Dcirc D subseteq U$?

general-topology uniform-spaces

share|cite|improve this question

asked Mar 14 at 17:15

user479859user479859

987

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  There are counterexamples. Look in good books on uniform spaces...
  $endgroup$
  – Henno Brandsma
  Mar 17 at 22:23
  

  
  
  
  

add a comment | 

$begingroup$

Let $X$ be a topological space but it is not uniform space and $U$ be a neighborhood of diagonal $X$, $Delta_X$. Is there a neighborhood $D(neq Delta_X)$ of $Delta_X$
such that $Dcirc D subseteq U$?

general-topology uniform-spaces

share|cite|improve this question

asked Mar 14 at 17:15

user479859user479859

987

$endgroup$

share|cite|improve this question

asked Mar 14 at 17:15

user479859user479859

987

share|cite|improve this question

asked Mar 14 at 17:15

user479859user479859

987

asked Mar 14 at 17:15

user479859user479859

987

asked Mar 14 at 17:15

user479859user479859

987