List questions from geometric-topology

Published on 05 Nov 2018 - 15:52

148

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Confusion about Heine-Borel property on manifold.

Published on 07 Nov 2018 - 5:02

40

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Separation from family of closed and connected subsets

Published on 08 Nov 2018 - 4:01

451

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Show that all open sets in $\mathbb{R}^n$ are the same for metrics $d_1,d_2,d_\infty$

Published on 08 Nov 2018 - 15:38

178

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Prove that $f$ is Morse function if an only if $det(H)^2 + \sum_{i=1}^k (\frac {\partial f}{\partial x_i})^2>0$(2)

Published on 10 Nov 2018 - 6:06

58

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Expansion of homeomorphism outside a disk

Published on 11 Nov 2018 - 14:33

256

Views

A difficulty in understanding the solution of problem 1.7.17 in Guillemin and Pollack.(p.47)

Published on 25 Mar 2026 - 6:12

160

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Understanding noncyclic covers of knot complements

Published on 25 Mar 2026 - 9:53

193

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Twisting the unit square n times before gluing( 2.1.6 in G&P).

Published on 25 Mar 2026 - 2:19

38

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Any spin $M^3$, exists a natural induced $\text{Pin}^-$ structure on Poincare dual PD

Published on 25 Mar 2026 - 14:25

490

Views

Proof for sphere eversion

Published on 18 Nov 2018 - 18:08

70

Views

How to show $\operatorname{Int}(z)$ is not empty?

Published on 25 Mar 2026 - 3:20

524

Views

If V and W are linear subspaces of $R^n$, then V transversal W means just $V + W = R^n$

Published on 25 Mar 2026 - 6:13

1.6k

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Locally compact in $\mathbb{R}^n$ and Hausdorff spaces

Published on 22 Nov 2018 - 15:31

271

Views

Representing a Multiple of the Fundamental Class of a Surface

Published on 23 Nov 2018 - 22:09

List Question

A difficulty in understanding a paragraph in p.41 in Guillemin & Pollack.

Confusion about Heine-Borel property on manifold.

Separation from family of closed and connected subsets

Show that all open sets in $\mathbb{R}^n$ are the same for metrics $d_1,d_2,d_\infty$

Prove that $f$ is Morse function if an only if $det(H)^2 + \sum_{i=1}^k (\frac {\partial f}{\partial x_i})^2>0$(2)

Expansion of homeomorphism outside a disk

A difficulty in understanding the solution of problem 1.7.17 in Guillemin and Pollack.(p.47)

Understanding noncyclic covers of knot complements

Twisting the unit square n times before gluing( 2.1.6 in G&P).

Any spin $M^3$, exists a natural induced $\text{Pin}^-$ structure on Poincare dual PD

Proof for sphere eversion

How to show $\operatorname{Int}(z)$ is not empty?

If V and W are linear subspaces of $R^n$, then V transversal W means just $V + W = R^n$

Locally compact in $\mathbb{R}^n$ and Hausdorff spaces

Representing a Multiple of the Fundamental Class of a Surface

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