Question

How can we show that $\left\{x\in\mathbb R^d:d(x,\Lambda^c)>\varepsilon\right\}\subseteq\Lambda$, if $\Lambda\subseteq\mathbb R^d$ is a domain?

score 25 · Answer 1 · 2026-04-15 03:37:31

25

Views

How can we show that $\left\{x\in\mathbb R^d:d(x,\Lambda^c)>\varepsilon\right\}\subseteq\Lambda$, if $\Lambda\subseteq\mathbb R^d$ is a domain?

Published on 15 Apr 2026 - 3:37

score 177 · Answer 2 · 2026-05-10 18:05:25

177

Views

Why is the velocity potential (in fluids) multi-valued in non-simply connected domains?

Published on 10 May 2026 - 18:05

score 127 · Answer 3 · 2026-05-10 14:06:47

127

Views

Coproduct of totally disconnected sets is totally disconnected.

Published on 10 May 2026 - 14:06

score 108 · Answer 4 · 2026-04-11 13:22:31

108

Views

Review of a connected set proof

Published on 11 Apr 2026 - 13:22

score 88 · Answer 5 · 2026-05-10 23:34:40

88

Views

Connected Set and Boundary Problem

Published on 10 May 2026 - 23:34

score 1.3k · Answer 6 · 2026-04-15 09:51:09

1.3k

Views

How to determine if a simple graph of $7$ vertices where the degree of each vertex is at least $3$ is connected?

Published on 15 Apr 2026 - 9:51

score 51 · Answer 7 · 2026-04-15 04:49:22

51

Views

To prove union of connected sets is not connected.

Published on 15 Apr 2026 - 4:49

score 52 · Answer 8 · 2026-05-10 13:48:56

52

Views

Connectedness of separated set (Topology)

Published on 10 May 2026 - 13:48

score 630 · Answer 9 · 2026-04-14 06:23:48

630

Views

Prob. 11, Sec. 24, in Munkres' TOPOLOGY, 2nd ed: Any example of a connected subspace with disconnected interior and boundary?

Published on 14 Apr 2026 - 6:23

score 57 · Answer 10 · 2026-05-10 23:53:36

57

Views

Show that $A∪B$ is connected

Published on 10 May 2026 - 23:53

score 187 · Answer 11 · 2026-04-11 20:59:47

187

Views

Multiply connected region

Published on 11 Apr 2026 - 20:59

score 120 · Answer 12 · 2026-04-14 19:50:35

120

Views

Disconnected sets in $\Bbb R^n$ and closed sets.

Published on 14 Apr 2026 - 19:50

score 1.7k · Answer 13 · 2026-05-10 17:02:25

1.7k

Views

Is the product of path connected spaces also path connected in a topology other than the product topology?

Published on 10 May 2026 - 17:02

score 195 · Answer 14 · 2026-04-09 04:55:30

195

Views

Trouble understanding a proof of topology (connectedness)

Published on 09 Apr 2026 - 4:55

score 392 · Answer 15 · 2026-04-17 13:49:12

392

Views

Every continuous function $f$ on the unit sphere (shell) has a point $p$ such that $f(p)=f(-p)$

Published on 17 Apr 2026 - 13:49

List Question

How can we show that $\left\{x\in\mathbb R^d:d(x,\Lambda^c)>\varepsilon\right\}\subseteq\Lambda$, if $\Lambda\subseteq\mathbb R^d$ is a domain?

Why is the velocity potential (in fluids) multi-valued in non-simply connected domains?

Coproduct of totally disconnected sets is totally disconnected.

Review of a connected set proof

Connected Set and Boundary Problem

How to determine if a simple graph of $7$ vertices where the degree of each vertex is at least $3$ is connected?

To prove union of connected sets is not connected.

Connectedness of separated set (Topology)

Prob. 11, Sec. 24, in Munkres' TOPOLOGY, 2nd ed: Any example of a connected subspace with disconnected interior and boundary?

Show that $A∪B$ is connected

Multiply connected region

Disconnected sets in $\Bbb R^n$ and closed sets.

Is the product of path connected spaces also path connected in a topology other than the product topology?

Trouble understanding a proof of topology (connectedness)

Every continuous function $f$ on the unit sphere (shell) has a point $p$ such that $f(p)=f(-p)$

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