List questions from differential-topology

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Topological space M with partition of unity--->M paracompact. John Lee Problems

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A surjective map which is not a submersion

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Qualifying Exam Question on Manifolds

Published on 08 Apr 2026 - 22:52

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Let $M$ and $N$ be smooth manifolds and $f: M\rightarrow N$ a diffeomorphism. Prove that the map $df:TM \rightarrow TN$ is a homeomorphism.

Published on 17 Apr 2026 - 8:49

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Uniqueness of Smoothed Corners

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Finding the kernel of Pushforward of $f:\mathbb R^n\rightarrow \mathbb R^k$

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Given that $X$ is closed and $Y$ is connected, prove that $Y$ is also closed.

Published on 14 Apr 2026 - 1:44

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How to prove that the map is open?

Published on 13 Apr 2026 - 5:50

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Compactness of covering space

Published on 14 Apr 2026 - 1:39

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What role does differentiability play in Topology?

Published on 17 Apr 2026 - 4:57

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"Product" bundle notation.

Published on 13 Apr 2026 - 10:27

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Given a local diffeomorphism $f: N \to M$ with $M$ orientable, then $N$ is orientable.

Published on 15 Apr 2026 - 3:28

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Extending a smooth map

Published on 09 Apr 2026 - 9:00

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Question about a specific case of the argument principle for maps of circles.

Published on 11 Apr 2026 - 19:00

List Question

Show that 2 sets are not homeomorphic

Topological space M with partition of unity--->M paracompact. John Lee Problems

A surjective map which is not a submersion

Qualifying Exam Question on Manifolds

Let $M$ and $N$ be smooth manifolds and $f: M\rightarrow N$ a diffeomorphism. Prove that the map $df:TM \rightarrow TN$ is a homeomorphism.

Uniqueness of Smoothed Corners

Finding the kernel of Pushforward of $f:\mathbb R^n\rightarrow \mathbb R^k$

Given that $X$ is closed and $Y$ is connected, prove that $Y$ is also closed.

How to prove that the map is open?

Compactness of covering space

What role does differentiability play in Topology?

"Product" bundle notation.

Given a local diffeomorphism $f: N \to M$ with $M$ orientable, then $N$ is orientable.

Extending a smooth map

Question about a specific case of the argument principle for maps of circles.

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