Question

Why are the finite-dimensional sets of $\mathbb{R}^{\infty}$ convergence-deterimining sets?

score 101 · Answer 1 · 2026-03-28 15:26:35

101

Views

Why are the finite-dimensional sets of $\mathbb{R}^{\infty}$ convergence-deterimining sets?

Published on 28 Mar 2026 - 15:26

score 676 · Answer 2 · 2018-12-29 19:24:12

676

Views

Prove that the dyadic rationals $D$ are dense in $\mathbb{Q}$

Published on 29 Dec 2018 - 19:24

score 797 · Answer 3 · 2026-03-29 13:29:04

797

Views

Assume $A \subset \mathbb{R}^n$ is connected such that $A^c$ is separated by $B,C$, then $A \cup B$ is connected.

Published on 29 Mar 2026 - 13:29

score 53 · Answer 4 · 2018-12-30 20:02:12

53

Views

extension of a homeomorphism to a compact pseudo metric space

Published on 30 Dec 2018 - 20:02

score 118 · Answer 5 · 2018-12-30 21:14:51

118

Views

Is there a metric on $\Bbb R$ based upon this measure of how close to odd and even a number is?

Published on 30 Dec 2018 - 21:14

score 520 · Answer 6 · 2026-03-25 16:08:28

520

Views

Proving $f(x)=(\cos(2\pi x),\sin(2\pi x)))$ is not closed and is the quotient mapping

Published on 25 Mar 2026 - 16:08

score 127 · Answer 7 · 2026-02-23 01:02:59

127

Views

Are uniformly equivalent metrics with the same bounded sets Holder equivalent?

Published on 23 Feb 2026 - 1:02

score 155 · Answer 8 · 2019-01-02 11:50:27

155

Views

If $f$ is the quotient mapping, is $(Y,\tau_1)$ metrizable?

Published on 02 Jan 2019 - 11:50

score 24 · Answer 9 · 2019-01-02 13:12:06

24

Views

If $\psi(x)=\int_U d(x,y)dy$, proof that there is a unique $x\in \Bbb R$ such that $\psi(x)$ is minimal?

Published on 02 Jan 2019 - 13:12

score 1k · Answer 10 · 2019-01-03 01:39:22

1k

Views

Are spaces shaped like the digits 0, 8 and 9 homeomorphic topological spaces?

Published on 03 Jan 2019 - 1:39

score 88 · Answer 11 · 2019-01-03 08:08:54

88

Views

Condition for equality of "distance to the boundary" and "distance to the set"

Published on 03 Jan 2019 - 8:08

score 1.1k · Answer 12 · 2019-01-03 20:51:51

1.1k

Views

Every bounded set $E\subseteq\mathbb{R}^2$ is contained in a disc of minimal radius

Published on 03 Jan 2019 - 20:51

score 1k · Answer 13 · 2026-03-25 01:20:21

1k

Views

Subgroup of Möbius transformations which are isometries with respect to the standard metric on the Riemann sphere

Published on 25 Mar 2026 - 1:20

score 102 · Answer 14 · 2019-01-04 02:55:27

102

Views

Relation in distance between a set $A$ and boundary of a set $B$, in this particular case.

Published on 04 Jan 2019 - 2:55

score 33 · Answer 15 · 2019-01-04 12:12:56

33

Views

Is $\mathbb{R}\setminus\{0\}$ endowed with $d(x,y)=|\frac{1}{x}-\frac{1}{y}|$ complete?

Published on 04 Jan 2019 - 12:12

List Question

Why are the finite-dimensional sets of $\mathbb{R}^{\infty}$ convergence-deterimining sets?

Prove that the dyadic rationals $D$ are dense in $\mathbb{Q}$

Assume $A \subset \mathbb{R}^n$ is connected such that $A^c$ is separated by $B,C$, then $A \cup B$ is connected.

extension of a homeomorphism to a compact pseudo metric space

Is there a metric on $\Bbb R$ based upon this measure of how close to odd and even a number is?

Proving $f(x)=(\cos(2\pi x),\sin(2\pi x)))$ is not closed and is the quotient mapping

Are uniformly equivalent metrics with the same bounded sets Holder equivalent?

If $f$ is the quotient mapping, is $(Y,\tau_1)$ metrizable?

If $\psi(x)=\int_U d(x,y)dy$, proof that there is a unique $x\in \Bbb R$ such that $\psi(x)$ is minimal?

Are spaces shaped like the digits 0, 8 and 9 homeomorphic topological spaces?

Condition for equality of "distance to the boundary" and "distance to the set"

Every bounded set $E\subseteq\mathbb{R}^2$ is contained in a disc of minimal radius

Subgroup of Möbius transformations which are isometries with respect to the standard metric on the Riemann sphere

Relation in distance between a set $A$ and boundary of a set $B$, in this particular case.

Is $\mathbb{R}\setminus\{0\}$ endowed with $d(x,y)=|\frac{1}{x}-\frac{1}{y}|$ complete?

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