Question

Where can I find out more about the nature of holes in plane regions?

score 87 · Answer 1 · 2026-04-15 08:38:57

87

Views

Where can I find out more about the nature of holes in plane regions?

Published on 15 Apr 2026 - 8:38

score 81 · Answer 2 · 2026-04-16 08:31:08

81

Views

If $X$ is a non empty closed subset of $\mathbb{R}$ and $Y = [1,2]$ then $X+Y$ is closed.

Published on 16 Apr 2026 - 8:31

score 239 · Answer 3 · 2026-04-16 04:56:54

239

Views

Let $f:R \rightarrow R$, be defined as $f(x)=x^2$.Show that the set$\{x:f(x)<1\}$ is an open set.

Published on 16 Apr 2026 - 4:56

score 1.3k · Answer 4 · 2026-04-14 18:04:12

1.3k

Views

If $f:\mathbb{R}\to\mathbb{R}$ is continuous and bijective. Is $f^{-1}:\mathbb{R}\to\mathbb{R}$ continuous?

Published on 14 Apr 2026 - 18:04

score 1.3k · Answer 5 · 2026-04-14 00:19:41

1.3k

Views

Improved intermediate value theorem

Published on 14 Apr 2026 - 0:19

score 237 · Answer 6 · 2026-04-12 23:36:39

237

Views

Proof Of Nested Interval Property implies Completeness

Published on 12 Apr 2026 - 23:36

score 70 · Answer 7 · 2026-04-15 08:54:12

70

Views

Distance making $(\mathbb{R} \setminus \mathbb{Z},d) $ complete and homeomorphic to $\mathbb{R}\times \mathbb{Z}$

Published on 15 Apr 2026 - 8:54

score 950 · Answer 8 · 2026-04-16 15:48:27

950

Views

Points of interest given $S=\{x>0:(x,\sin(1/x)\in \mathbb R^2\}$

Published on 16 Apr 2026 - 15:48

score 293 · Answer 9 · 2026-03-25 20:36:02

293

Views

One-point compactification and the existence of a contractible open neighborhood of infinity

Published on 25 Mar 2026 - 20:36

score 29 · Answer 10 · 2026-04-13 09:12:52

29

Views

How does $\mathscr B$ and $\mathscr B'$ are equivalent?

Published on 13 Apr 2026 - 9:12

score 7.2k · Answer 11 · 2026-04-10 19:00:20

7.2k

Views

Proof of 1/n (where n is from Natural Numbers) as neither open nor closed?

Published on 10 Apr 2026 - 19:00

score 468 · Answer 12 · 2026-04-11 12:03:25

468

Views

Set which is locally $\iota-$null but not $\iota$-null

Published on 11 Apr 2026 - 12:03

score 25 · Answer 13 · 2026-04-11 11:28:13

25

Views

uniformly discrete in one metric but not in the other giving the same topology

Published on 11 Apr 2026 - 11:28

score 438 · Answer 14 · 2026-04-17 05:52:19

438

Views

When we say that $\mathbb S^1$ is compact, which topology we are thinking about?

Published on 17 Apr 2026 - 5:52

score 200 · Answer 15 · 2026-04-13 07:03:30

200

Views

Stone–Weierstrass theorem with exact matches at a finite number of points

Published on 13 Apr 2026 - 7:03

List Question

Where can I find out more about the nature of holes in plane regions?

If $X$ is a non empty closed subset of $\mathbb{R}$ and $Y = [1,2]$ then $X+Y$ is closed.

Let $f:R \rightarrow R$, be defined as $f(x)=x^2$.Show that the set$\{x:f(x)<1\}$ is an open set.

If $f:\mathbb{R}\to\mathbb{R}$ is continuous and bijective. Is $f^{-1}:\mathbb{R}\to\mathbb{R}$ continuous?

Improved intermediate value theorem

Proof Of Nested Interval Property implies Completeness

Distance making $(\mathbb{R} \setminus \mathbb{Z},d) $ complete and homeomorphic to $\mathbb{R}\times \mathbb{Z}$

Points of interest given $S=\{x>0:(x,\sin(1/x)\in \mathbb R^2\}$

One-point compactification and the existence of a contractible open neighborhood of infinity

How does $\mathscr B$ and $\mathscr B'$ are equivalent?

Proof of 1/n (where n is from Natural Numbers) as neither open nor closed?

Set which is locally $\iota-$null but not $\iota$-null

uniformly discrete in one metric but not in the other giving the same topology

When we say that $\mathbb S^1$ is compact, which topology we are thinking about?

Stone–Weierstrass theorem with exact matches at a finite number of points

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