Question

Proof of Theorem 16.4 in Munkres Topology 2nd Edition

score 199 · Answer 1 · 2018-06-21 17:47:57

Proof of Theorem 16.4 in Munkres Topology 2nd Edition

Published on 21 Jun 2018 - 17:47

score 88 · Answer 2 · 2018-06-21 18:03:43

If an open, continuous function $f:\mathbb{R}^n\rightarrow\mathbb{R}^n$ is one-to-one on a set of bounded complement, is $f$ one-to-one everywhere?

score 862 · Answer 3 · 2026-04-02 20:17:10

862

Views

Coarsest topology where a function is continuous

Published on 02 Apr 2026 - 20:17

score 686 · Answer 4 · 2026-03-28 00:35:18

686

Views

Empty Cartesian Product, what is $\mathbb{R}^0$?

Published on 28 Mar 2026 - 0:35

score 150 · Answer 5 · 2026-04-01 12:55:16

150

Views

Does $dist(x, \partial A) \leq dist(x, \partial B)$ if $x \in A \subset B$?

Published on 01 Apr 2026 - 12:55

score 67 · Answer 6 · 2026-03-25 03:02:36

67

Views

How can every continuous function be measurable if topologies can contain an uncountable number of open sets?

Published on 25 Mar 2026 - 3:02

score 781 · Answer 7 · 2018-06-22 06:28:01

781

Views

Isn't basic open cover same as an open cover?

Published on 22 Jun 2018 - 6:28

score 66 · Answer 8 · 2018-06-22 10:25:34

66

Views

Given two dense disjoint subsests their interior is empty

Published on 22 Jun 2018 - 10:25

score 67 · Answer 9 · 2026-03-26 22:17:34

67

Views

Order of Two Operators

Published on 26 Mar 2026 - 22:17

score 59 · Answer 10 · 2026-03-25 01:36:18

59

Views

Consider $\mathbb{R}^3/E$ with $E = \{(x,y,z) \in \mathbb{R}^2 \vert x^2 + y^2 + z^2 \leq 1\}$

Published on 25 Mar 2026 - 1:36

score 106 · Answer 11 · 2026-03-25 20:59:56

106

Views

Some properties vector bundles and Thom spaces

Published on 25 Mar 2026 - 20:59

score 712 · Answer 12 · 2026-03-26 14:43:20

712

Views

Linear subspace of codimension one in infinite dimensional Banach space

Published on 26 Mar 2026 - 14:43

score 825 · Answer 13 · 2026-04-02 20:07:25

825

Views

Continuous function on $[0,1]$, $f(0)=f(1)$

Published on 02 Apr 2026 - 20:07

score 301 · Answer 14 · 2026-03-27 16:54:02

301

Views

Proof of Theorem 9.2 in Brezis' Functional Analysis, Sobolev spaces and Partial Differential Equations

Published on 27 Mar 2026 - 16:54

score 181 · Answer 15 · 2018-06-22 18:00:35

181

Views

A strictly decreasing nested sequence of non-empty compact subsets of S has a non-empty intersection with empty interior.

Published on 22 Jun 2018 - 18:00

List Question

Proof of Theorem 16.4 in Munkres Topology 2nd Edition

If an open, continuous function $f:\mathbb{R}^n\rightarrow\mathbb{R}^n$ is one-to-one on a set of bounded complement, is $f$ one-to-one everywhere?

Coarsest topology where a function is continuous

Empty Cartesian Product, what is $\mathbb{R}^0$?

Does $dist(x, \partial A) \leq dist(x, \partial B)$ if $x \in A \subset B$?

How can every continuous function be measurable if topologies can contain an uncountable number of open sets?

Isn't basic open cover same as an open cover?

Given two dense disjoint subsests their interior is empty

Order of Two Operators

Consider $\mathbb{R}^3/E$ with $E = \{(x,y,z) \in \mathbb{R}^2 \vert x^2 + y^2 + z^2 \leq 1\}$

Some properties vector bundles and Thom spaces

Linear subspace of codimension one in infinite dimensional Banach space

Continuous function on $[0,1]$, $f(0)=f(1)$

Proof of Theorem 9.2 in Brezis' Functional Analysis, Sobolev spaces and Partial Differential Equations

A strictly decreasing nested sequence of non-empty compact subsets of S has a non-empty intersection with empty interior.

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