Question

Why $T_{A}M(n) = M(n)$ and why $T_{f(A)}S(n) = S(n)$ and why $M(n)$ & $S(n)$ are manifolds. (Guillemin & Pollack p.23)

score 56 · Answer 1 · 2026-04-17 03:21:56

56

Views

Why $T_{A}M(n) = M(n)$ and why $T_{f(A)}S(n) = S(n)$ and why $M(n)$ & $S(n)$ are manifolds. (Guillemin & Pollack p.23)

Published on 17 Apr 2026 - 3:21

score 132 · Answer 2 · 2026-04-11 03:08:50

132

Views

Is there a unnecessary part in this definition of "not connected set" in complex plane?

Published on 11 Apr 2026 - 3:08

score 542 · Answer 3 · 2026-04-14 11:52:54

542

Views

Product topology Vs cofinite topology

Published on 14 Apr 2026 - 11:52

score 144 · Answer 4 · 2026-04-16 13:14:54

144

Views

Can the (extended) Möbius strip be found as the torus $T^2$ minus some embedded $S^1$?

Published on 16 Apr 2026 - 13:14

score 1.4k · Answer 5 · 2026-04-15 11:21:24

1.4k

Views

If the intersection of an open set with a closed set is non-empty....

Published on 15 Apr 2026 - 11:21

score 107 · Answer 6 · 2026-04-11 14:55:16

107

Views

For every subset $A$ of $X$, $f(\overline{A})$ is a subset of $\overline{f(A)}$

Published on 11 Apr 2026 - 14:55

score 759 · Answer 7 · 2026-04-09 19:02:37

759

Views

Boundary of set equal the same set

Published on 09 Apr 2026 - 19:02

score 582 · Answer 8 · 2026-04-14 23:58:19

582

Views

Sequential compactness of $S_\Omega$ and unbounded sequences.

Published on 14 Apr 2026 - 23:58

score 104 · Answer 9 · 2026-04-12 05:14:59

104

Views

A difficulty in the proof of partial converse I.(p. 24 in Guillemin & Pollack)

Published on 12 Apr 2026 - 5:14

score 1.7k · Answer 10 · 2026-04-15 22:42:51

1.7k

Views

Prove the quotient map of real projective n space is smooth

Published on 15 Apr 2026 - 22:42

score 257 · Answer 11 · 2026-04-15 20:24:33

257

Views

Prove that $\mathscr B$ is a basis for topology $\mathscr T$ on $\mathbb R$. Is $\mathscr T$ is a usual topology on $\mathbb R$?

Published on 15 Apr 2026 - 20:24

score 150 · Answer 12 · 2026-04-11 12:03:20

150

Views

Application of Banach contraction principle

Published on 11 Apr 2026 - 12:03

score 731 · Answer 13 · 2026-04-12 12:16:22

731

Views

Path connectedness of comb space

Published on 12 Apr 2026 - 12:16

score 275 · Answer 14 · 2026-04-13 00:18:23

275

Views

If the graphic of $f : X \to Y$ is closed with $Y$ compact and Hausdorff, then $f$ is continuous. [Proof Verification]

Published on 13 Apr 2026 - 0:18

score 326 · Answer 15 · 2026-03-24 23:43:12

326

Views

Doe a smooth function map positive measure sets to positive measure sets

Published on 24 Mar 2026 - 23:43

List Question

Why $T_{A}M(n) = M(n)$ and why $T_{f(A)}S(n) = S(n)$ and why $M(n)$ & $S(n)$ are manifolds. (Guillemin & Pollack p.23)

Is there a unnecessary part in this definition of "not connected set" in complex plane?

Product topology Vs cofinite topology

Can the (extended) Möbius strip be found as the torus $T^2$ minus some embedded $S^1$?

If the intersection of an open set with a closed set is non-empty....

For every subset $A$ of $X$, $f(\overline{A})$ is a subset of $\overline{f(A)}$

Boundary of set equal the same set

Sequential compactness of $S_\Omega$ and unbounded sequences.

A difficulty in the proof of partial converse I.(p. 24 in Guillemin & Pollack)

Prove the quotient map of real projective n space is smooth

Prove that $\mathscr B$ is a basis for topology $\mathscr T$ on $\mathbb R$. Is $\mathscr T$ is a usual topology on $\mathbb R$?

Application of Banach contraction principle

Path connectedness of comb space

If the graphic of $f : X \to Y$ is closed with $Y$ compact and Hausdorff, then $f$ is continuous. [Proof Verification]

Doe a smooth function map positive measure sets to positive measure sets

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