Question

Does there always exist a continuous map saturating a given open set?

score 105 · Answer 1 · 2026-04-12 07:48:20

105

Views

Does there always exist a continuous map saturating a given open set?

Published on 12 Apr 2026 - 7:48

score 54 · Answer 2 · 2026-05-10 22:04:43

54

Views

Guesses on fixed point existence

Published on 10 May 2026 - 22:04

score 785 · Answer 3 · 2026-04-16 04:43:52

785

Views

Prove that quotient maps $q$ are characterized by $f:Y\to Z$ being continuous iff $f\circ q$ is

Published on 16 Apr 2026 - 4:43

score 38 · Answer 4 · 2026-04-14 04:45:41

38

Views

Proving [0,1] is not compact with a particular topology

Published on 14 Apr 2026 - 4:45

score 90 · Answer 5 · 2026-04-17 13:39:30

90

Views

Connected component of $\{(x_1,...,x_n) \; | \; x_1^2+...+{x_{n-1}}^2-x_n^2 \neq 0\}$

Published on 17 Apr 2026 - 13:39

score 294 · Answer 6 · 2026-04-13 17:34:46

294

Views

Compact spaces in which any closed set can be partitioned into finitely many closed sets whose clopen subsets extend to the whole space

Published on 13 Apr 2026 - 17:34

score 1.1k · Answer 7 · 2026-04-13 00:50:52

1.1k

Views

homeomorphic image of an simply connected set

Published on 13 Apr 2026 - 0:50

score 221 · Answer 8 · 2026-04-11 22:35:52

221

Views

Why is compactness important to find solution of certain problems?

Published on 11 Apr 2026 - 22:35

score 485 · Answer 9 · 2026-05-11 09:28:42

485

Views

Open dense subset of $\mathbb{R}$.

Published on 11 May 2026 - 9:28

score 334 · Answer 10 · 2026-05-10 19:13:01

334

Views

Serre says open covers do not form a set, why? Directed sets and limits.

Published on 10 May 2026 - 19:13

score 170 · Answer 11 · 2026-05-11 04:39:09

170

Views

Proving $(-1,1)^{\mathbb{N}}$ is not open in the product topology of $\mathbb{R}^{\mathbb{N}}$

Published on 11 May 2026 - 4:39

score 114 · Answer 12 · 2026-04-16 09:16:19

Proving that $\displaystyle\{{(x_n, y_n) \}}_{n \in \mathbb{N}}$ converges to $(x,y)$ on the product topology iff $x_n \to x$ and $y_ n \to y$

score 56 · Answer 13 · 2026-04-17 09:30:54

$K = \{A \in \Bbb M_n (\Bbb R)\ |\ A=A^T, \mathrm {tr} (A) = 1, x^TAx \ge 0\ \text {for all}\ x \in \Bbb R^n \}$ is compact or not?

score 104 · Answer 14 · 2026-04-17 08:40:50

104

Views

If $X$ is a real normed linear space and $r>0$, then $B_{r}(x_0+y_0)=B_{r}(y_0)+\{x_0\}$ for fixed $x_0,\,y_0\in X.$

Published on 17 Apr 2026 - 8:40

score 169 · Answer 15 · 2026-05-10 18:29:28

169

Views

Order Topology on a Preorder

Published on 10 May 2026 - 18:29

List Question

Does there always exist a continuous map saturating a given open set?

Guesses on fixed point existence

Prove that quotient maps $q$ are characterized by $f:Y\to Z$ being continuous iff $f\circ q$ is

Proving [0,1] is not compact with a particular topology

Connected component of $\{(x_1,...,x_n) \; | \; x_1^2+...+{x_{n-1}}^2-x_n^2 \neq 0\}$

Compact spaces in which any closed set can be partitioned into finitely many closed sets whose clopen subsets extend to the whole space

homeomorphic image of an simply connected set

Why is compactness important to find solution of certain problems?

Open dense subset of $\mathbb{R}$.

Serre says open covers do not form a set, why? Directed sets and limits.

Proving $(-1,1)^{\mathbb{N}}$ is not open in the product topology of $\mathbb{R}^{\mathbb{N}}$

Proving that $\displaystyle\{{(x_n, y_n) \}}_{n \in \mathbb{N}}$ converges to $(x,y)$ on the product topology iff $x_n \to x$ and $y_ n \to y$

$K = \{A \in \Bbb M_n (\Bbb R)\ |\ A=A^T, \mathrm {tr} (A) = 1, x^TAx \ge 0\ \text {for all}\ x \in \Bbb R^n \}$ is compact or not?

If $X$ is a real normed linear space and $r>0$, then $B_{r}(x_0+y_0)=B_{r}(y_0)+\{x_0\}$ for fixed $x_0,\,y_0\in X.$

Order Topology on a Preorder

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