Question

Separating two sets in normal topological spaces by binary relations

score 54 · Answer 1 · 2016-07-12 13:15:39

54

Views

Separating two sets in normal topological spaces by binary relations

Published on 12 Jul 2016 - 13:15

score 107 · Answer 2 · 2016-07-13 08:57:01

107

Views

Product of perfectly-$T_2$ spaces

Published on 13 Jul 2016 - 8:57

score 82 · Answer 3 · 2016-07-14 07:49:03

82

Views

Product of perfectly-$T_3$ spaces

Published on 14 Jul 2016 - 7:49

score 2.1k · Answer 4 · 2016-07-17 22:24:02

2.1k

Views

Show that any metrizable space $X$ is Hausdorff

Published on 17 Jul 2016 - 22:24

score 297 · Answer 5 · 2016-07-18 18:54:41

297

Views

Example of Kolmogorov space which is neither Fréchet nor sober

Published on 18 Jul 2016 - 18:54

score 487 · Answer 6 · 2016-07-19 04:34:18

487

Views

Alternative proof: show that any metrizable space $X$ is normal - Part 1

Published on 19 Jul 2016 - 4:34

score 37 · Answer 7 · 2016-07-20 18:24:52

37

Views

About normal spaces and proximities

Published on 20 Jul 2016 - 18:24

score 178 · Answer 8 · 2016-07-23 14:46:45

178

Views

$X$ be a Hausdorff topological space , let $f:X \to X$ be a continuous map such that $f\circ f=f$ , then is $f(X)$ is closed in $X$ ?

Published on 23 Jul 2016 - 14:46

score 92 · Answer 9 · 2016-07-24 21:12:28

92

Views

Necessary and Sufficient Condition for Complete Regularity of Topological Space

Published on 24 Jul 2016 - 21:12

score 1.6k · Answer 10 · 2016-07-30 02:22:48

1.6k

Views

How many compact Hausdorff spaces are there of a given cardinality?

Published on 30 Jul 2016 - 2:22

score 784 · Answer 11 · 2016-07-31 23:03:22

784

Views

Under which $T$ axiom can you separate disjoint closed and compact set? Compact and compact set?

Published on 31 Jul 2016 - 23:03

score 363 · Answer 12 · 2016-08-06 20:43:30

363

Views

Why in discrete space, $\{x\}$ is open $\Rightarrow$ $\{x\}$ is closed, but in $T_1$ space, $\{x\}$ is closed $\not\Rightarrow$ $\{x\}$ is open?

Published on 06 Aug 2016 - 20:43

score 1.3k · Answer 13 · 2016-08-08 01:28:09

1.3k

Views

Show $A \subseteq X$, $X$ normal, is separated by a continuous function iff $A$ is closed $G_\delta$

Published on 08 Aug 2016 - 1:28

score 348 · Answer 14 · 2016-08-09 16:23:45

348

Views

What topologies on $\mathbb{Z}$ make the floor function continous?

Published on 09 Aug 2016 - 16:23

score 49 · Answer 15 · 2016-08-10 15:45:50

49

Views

$X$ non-degenerate Hausdorff space , $f:[0,1] \to X$ is surjective continuous , $a:=\inf \{y\in (0,1]: f([0,y])=X\}$ , then is $a>0$ and $f([0,a])=X$?

Published on 10 Aug 2016 - 15:45

List Question

Separating two sets in normal topological spaces by binary relations

Product of perfectly-$T_2$ spaces

Product of perfectly-$T_3$ spaces

Show that any metrizable space $X$ is Hausdorff

Example of Kolmogorov space which is neither Fréchet nor sober

Alternative proof: show that any metrizable space $X$ is normal - Part 1

About normal spaces and proximities

$X$ be a Hausdorff topological space , let $f:X \to X$ be a continuous map such that $f\circ f=f$ , then is $f(X)$ is closed in $X$ ?

Necessary and Sufficient Condition for Complete Regularity of Topological Space

How many compact Hausdorff spaces are there of a given cardinality?

Under which $T$ axiom can you separate disjoint closed and compact set? Compact and compact set?

Why in discrete space, $\{x\}$ is open $\Rightarrow$ $\{x\}$ is closed, but in $T_1$ space, $\{x\}$ is closed $\not\Rightarrow$ $\{x\}$ is open?

Show $A \subseteq X$, $X$ normal, is separated by a continuous function iff $A$ is closed $G_\delta$

What topologies on $\mathbb{Z}$ make the floor function continous?

$X$ non-degenerate Hausdorff space , $f:[0,1] \to X$ is surjective continuous , $a:=\inf \{y\in (0,1]: f([0,y])=X\}$ , then is $a>0$ and $f([0,a])=X$?

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