List questions from manifolds-with-boundary

Published on 26 Mar 2026 - 6:07

65

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The set that we add to compactify is itself compact.

Published on 15 Dec 2017 - 13:17

220

Views

Stokes' theorem proof without FTC

Published on 16 Dec 2017 - 1:44

535

Views

What are the possible boundaries of connected compact manifolds?

Published on 26 Mar 2026 - 2:55

443

Views

Show that if $dF_p$ is nonsingular, then $F(p)\in \text{Int}N$ : Lee's Smooth Manifolds

Published on 27 Mar 2026 - 7:50

721

Views

Show that $\mathbb{S}^d$ is homeomorphic to the the boundary of the cube $\partial I^{d+1}$.

Published on 31 Dec 2017 - 5:57

375

Views

Showing that a neighborhood is not homeomorphic to the open subset of $R^n$

Published on 05 Jan 2018 - 5:29

2.4k

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The definition of submanifold of a manifold with boundary

Published on 08 Sep 2011 - 8:29

190

Views

How can we show that this normal field is "outward pointing"?

Published on 26 Mar 2026 - 21:34

76

Views

Characterization of $C^\alpha$-differentiability on a submanifold with boundary

Published on 26 Mar 2026 - 16:05

240

Views

Definition of the tangent space for a submanifold with boundary in terms of regular curves

Published on 26 Mar 2026 - 23:10

256

Views

Show that for a properly embedded submanifold the manifold and topogoical boundary coincide

Published on 08 Aug 2020 - 8:14

826

Views

If $\partial\Omega$ is of class $C^1$, does it need to be the boundary of a $C^1$-regular domain?

Published on 08 Aug 2020 - 9:56

889

Views

Lee Smooth Manifolds Problem 1-11 - $\overline{\mathbb B}^n$ is a smooth manifold with boundary

Published on 11 Aug 2020 - 15:09

50

Views

Convexity condition for smooth submanifold-with-boundary in $\mathbb{R}^n$

Published on 12 Aug 2020 - 13:45

List Question

Are there topological manifolds with boundary that are not compact?

The set that we add to compactify is itself compact.

Stokes' theorem proof without FTC

What are the possible boundaries of connected compact manifolds?

Show that if $dF_p$ is nonsingular, then $F(p)\in \text{Int}N$ : Lee's Smooth Manifolds

Show that $\mathbb{S}^d$ is homeomorphic to the the boundary of the cube $\partial I^{d+1}$.

Showing that a neighborhood is not homeomorphic to the open subset of $R^n$

The definition of submanifold of a manifold with boundary

How can we show that this normal field is "outward pointing"?

Characterization of $C^\alpha$-differentiability on a submanifold with boundary

Definition of the tangent space for a submanifold with boundary in terms of regular curves

Show that for a properly embedded submanifold the manifold and topogoical boundary coincide

If $\partial\Omega$ is of class $C^1$, does it need to be the boundary of a $C^1$-regular domain?

Lee Smooth Manifolds Problem 1-11 - $\overline{\mathbb B}^n$ is a smooth manifold with boundary

Convexity condition for smooth submanifold-with-boundary in $\mathbb{R}^n$

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