User JonSK

5 votes

2 answers

842 views

Immersions are open maps if dimensions are equal

differential-geometry differential-topology

asked Apr 4, 2016 at 5:25

4 votes

1 answer

475 views

If $M$ is a connected manifold, does $M\setminus\{p\}$ have finitely many components?

general-topology differential-topology

asked Apr 7, 2016 at 21:34

4 votes

1 answer

132 views

How to show if these spaces are metrizable?

general-topology

asked Jan 3, 2016 at 2:04

4 votes

1 answer

202 views

Product of perfect maps is perfect

general-topology

asked Jan 21, 2016 at 4:38

3 votes

1 answer

82 views

Proving that $\mathbb{R}P^n$ is a manifold

differential-geometry differential-topology

asked Feb 27, 2016 at 20:03

3 votes

1 answer

377 views

Alternative definitions of residue at infinity

complex-analysis

asked Jan 13, 2016 at 1:05

3 votes

2 answers

148 views

If $\mu(A)<\delta$ then $\sup_{f\in\mathcal{F}}\int_A|f|d\mu<\epsilon$

measure-theory

asked Jan 15, 2016 at 0:48

2 votes

1 answer

297 views

Prove that $\int fg=\lim_{n\to\infty}\int f_ng$ [duplicate]

measure-theory

asked Jan 14, 2016 at 3:10

2 votes

1 answer

169 views

Extending differentiable functions to the whole manifold

differential-geometry differential-topology

asked Feb 29, 2016 at 2:57

2 votes

1 answer

305 views

Is it true that $Fr(A\cup B)=Fr(A)\cup Fr(B)$ if $A\cap\overline{B}=\emptyset$ and $\overline{A}\cap B=\emptyset$?

general-topology

asked Jan 7, 2016 at 4:04

2 votes

1 answer

153 views

Show that $C=\cap_{s\in S}C_s$ is compact, connected and non-empty. [duplicate]

general-topology

asked Jan 20, 2016 at 4:16

2 votes

0 answers

325 views

Showing that $\{(x,|x|):x\in\mathbb{R}\}$ is not the image of an immersion [duplicate]

differential-geometry differential-topology

asked Mar 25, 2016 at 21:58

2 votes

1 answer

48 views

Isometries of metric spaces $Z=X\cup (X\times\mathbb{R})$ (corrected)

general-topology metric-spaces

asked Mar 28, 2016 at 23:39

1 vote

0 answers

616 views

How to show this atlas is maximal on the sphere $S^n$?

differential-geometry differential-topology

asked Feb 25, 2016 at 17:10

1 vote

2 answers

110 views

If we have a basis $\{f_1,...,f_n\}$ of $V^*$, can we give a basis $\{x_1,...,x_n\}$ of $V$?

linear-algebra

asked Apr 9, 2016 at 18:41

1 vote

1 answer

37 views

Isometries of $(\mathbb{R},\min\{|\cdot|,1\})$

real-analysis general-topology

asked Apr 13, 2016 at 20:30

1 vote

1 answer

124 views

If $X$ is locally compact, $U$ is open and $F$ is closed, is $U\cap F$ locally compact?

general-topology

asked Jan 23, 2016 at 1:57

1 vote

1 answer

144 views

A particular case of Sard's Theorem

differential-geometry differential-topology

asked Mar 21, 2016 at 21:58

1 vote

2 answers

143 views

Uniform metric topology is contained in box topology

general-topology

asked Jan 6, 2016 at 2:20

1 vote

2 answers

178 views

Calculating $\int_{|z|=2}\frac{e^{1/z^2}}{1-z}dz$

complex-analysis

asked Jan 17, 2016 at 4:52

1 vote

1 answer

42 views

Showing that $\lim_{t\to\infty}\left(\sup_{n\in\mathbb{N}}\int_{\{x:f_n(x)\ge t\}}|f_n|d\mu\right)=0.$

measure-theory

asked Jan 17, 2016 at 18:26

1 vote

1 answer

106 views

If $\lambda, v$ are two measures, is $\{A:v(A)=\lambda(A)\}$ a $\sigma-$algebra?

measure-theory

asked Jan 18, 2016 at 2:53

0 votes

1 answer

109 views

Show that $|f(z)|\le M\frac{\prod_{k=1}^n|z-z_k|}{\prod_{k=1}^n|z+\overline{z_k}|}$ on the right half plane

complex-analysis

asked Jan 16, 2016 at 21:36

0 votes

1 answer

443 views

Proving that the tangent space of $\Delta$ is the diagonal of $T_pM\times T_pM$

differential-geometry differential-topology

asked Feb 28, 2016 at 18:37

0 votes

1 answer

70 views

If $G$ is a discrete topological group, is $(G,X,\theta)$ a $G$-space?

general-topology topological-groups

asked Feb 20, 2016 at 17:20

0 votes

1 answer

289 views

Cluster and limit points of $z$-ultrafilters

general-topology

asked Apr 24, 2016 at 20:46

0 votes

1 answer

332 views

Exhaustion by compact sets in $\mathbb{C}^n$

real-analysis general-topology complex-analysis

asked Apr 29, 2016 at 5:23

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27 Questions

Immersions are open maps if dimensions are equal

If $M$ is a connected manifold, does $M\setminus\{p\}$ have finitely many components?

How to show if these spaces are metrizable?

Product of perfect maps is perfect

Proving that $\mathbb{R}P^n$ is a manifold

Alternative definitions of residue at infinity

If $\mu(A)<\delta$ then $\sup_{f\in\mathcal{F}}\int_A|f|d\mu<\epsilon$

Prove that $\int fg=\lim_{n\to\infty}\int f_ng$ [duplicate]

Extending differentiable functions to the whole manifold

Is it true that $Fr(A\cup B)=Fr(A)\cup Fr(B)$ if $A\cap\overline{B}=\emptyset$ and $\overline{A}\cap B=\emptyset$?

Show that $C=\cap_{s\in S}C_s$ is compact, connected and non-empty. [duplicate]

Showing that $\{(x,|x|):x\in\mathbb{R}\}$ is not the image of an immersion [duplicate]

Isometries of metric spaces $Z=X\cup (X\times\mathbb{R})$ (corrected)

How to show this atlas is maximal on the sphere $S^n$?

If we have a basis $\{f_1,...,f_n\}$ of $V^*$, can we give a basis $\{x_1,...,x_n\}$ of $V$?

Isometries of $(\mathbb{R},\min\{|\cdot|,1\})$

If $X$ is locally compact, $U$ is open and $F$ is closed, is $U\cap F$ locally compact?

A particular case of Sard's Theorem

Uniform metric topology is contained in box topology

Calculating $\int_{|z|=2}\frac{e^{1/z^2}}{1-z}dz$

Showing that $\lim_{t\to\infty}\left(\sup_{n\in\mathbb{N}}\int_{\{x:f_n(x)\ge t\}}|f_n|d\mu\right)=0.$

If $\lambda, v$ are two measures, is $\{A:v(A)=\lambda(A)\}$ a $\sigma-$algebra?

Show that $|f(z)|\le M\frac{\prod_{k=1}^n|z-z_k|}{\prod_{k=1}^n|z+\overline{z_k}|}$ on the right half plane

Proving that the tangent space of $\Delta$ is the diagonal of $T_pM\times T_pM$

If $G$ is a discrete topological group, is $(G,X,\theta)$ a $G$-space?

Cluster and limit points of $z$-ultrafilters

Exhaustion by compact sets in $\mathbb{C}^n$