Question

Find continuous functions $f,g$ such that $g\circ f $ is closed and continuous but neither $g$ nor $f$ is closed map.

score 104 · Answer 1 · 2026-05-10 19:55:38

104

Views

Find continuous functions $f,g$ such that $g\circ f $ is closed and continuous but neither $g$ nor $f$ is closed map.

Published on 10 May 2026 - 19:55

score 58 · Answer 2 · 2026-05-10 16:11:58

58

Views

Canonical projections for $\mathbb{H}^2_1$ and $\mathbb{S}^2_1$

Published on 10 May 2026 - 16:11

score 237 · Answer 3 · 2026-05-12 19:21:38

237

Views

$\mathscr{B} = \{ [a, b) | a< b \in \mathbb{R} \}$ is a basis for a Topology in $\mathbb{R}$

Published on 12 May 2026 - 19:21

score 106 · Answer 4 · 2026-04-17 04:11:06

106

Views

Is $[1,5]$ an open set?

Published on 17 Apr 2026 - 4:11

score 1.2k · Answer 5 · 2026-04-13 23:28:39

1.2k

Views

Proving the No Retraction Theorem

Published on 13 Apr 2026 - 23:28

score 49 · Answer 6 · 2026-04-14 02:31:11

49

Views

Is it true that for any metrics, $f(\lambda)=\lambda x+(1-\lambda) y$ is continuous where $\lambda \in \mathbb{R}, x,y \in \mathbb{R}^n$?

Published on 14 Apr 2026 - 2:31

score 1.1k · Answer 7 · 2026-04-11 15:59:10

1.1k

Views

Norm and Weak Topologies agree?

Published on 11 Apr 2026 - 15:59

score 179 · Answer 8 · 2026-04-09 20:37:46

179

Views

Exercise on topology on the natural numbers induced by a Kuratowski closure operator

Published on 09 Apr 2026 - 20:37

score 211 · Answer 9 · 2026-04-14 21:10:53

211

Views

How many non-homeomorphic topological structures are there on a finite set of order $n$?

Published on 14 Apr 2026 - 21:10

score 112 · Answer 10 · 2026-04-13 21:37:19

Is there a counterexample such that : $X$ is a topology space , every infinite subset of $X$ has a limit point but $X$ is not compact .

score 124 · Answer 11 · 2026-04-11 16:03:12

124

Views

Continuous function (Topology)

Published on 11 Apr 2026 - 16:03

score 52 · Answer 12 · 2026-04-16 14:44:26

52

Views

Jordan curve; is the inside mapped to the inside by a homeomorphism?

Published on 16 Apr 2026 - 14:44

score 174 · Answer 13 · 2026-05-10 13:50:28

174

Views

Space of Riemannian metrics as a topological groupoid

Published on 10 May 2026 - 13:50

score 42 · Answer 14 · 2026-04-10 20:57:19

42

Views

What if every nontrivial closed subset is compact?

Published on 10 Apr 2026 - 20:57

score 51 · Answer 15 · 2026-04-14 09:20:35

51

Views

In topological proofs, are any subsets mentioned always subsets comprising the topology?

Published on 14 Apr 2026 - 9:20

List Question

Find continuous functions $f,g$ such that $g\circ f $ is closed and continuous but neither $g$ nor $f$ is closed map.

Canonical projections for $\mathbb{H}^2_1$ and $\mathbb{S}^2_1$

$\mathscr{B} = \{ [a, b) | a< b \in \mathbb{R} \}$ is a basis for a Topology in $\mathbb{R}$

Is $[1,5]$ an open set?

Proving the No Retraction Theorem

Is it true that for any metrics, $f(\lambda)=\lambda x+(1-\lambda) y$ is continuous where $\lambda \in \mathbb{R}, x,y \in \mathbb{R}^n$?

Norm and Weak Topologies agree?

Exercise on topology on the natural numbers induced by a Kuratowski closure operator

How many non-homeomorphic topological structures are there on a finite set of order $n$?

Is there a counterexample such that : $X$ is a topology space , every infinite subset of $X$ has a limit point but $X$ is not compact .

Continuous function (Topology)

Jordan curve; is the inside mapped to the inside by a homeomorphism?

Space of Riemannian metrics as a topological groupoid

What if every nontrivial closed subset is compact?

In topological proofs, are any subsets mentioned always subsets comprising the topology?

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