Question

Unit ball in $l^{2}$ is bounded and closed but not compact.

score 2.5k · Answer 1 · 2026-03-25 07:42:53

Unit ball in $l^{2}$ is bounded and closed but not compact.

Published on 25 Mar 2026 - 7:42

score 39 · Answer 2 · 2018-03-16 03:22:05

Is $X$ a $T_1$ space? (i.e., given a pair of distinct points in $X$, does each one of them have a neighborhood not containing the other?)

score 585 · Answer 3 · 2018-03-16 03:42:50

585

Views

Let $\mathbb{R}$ with cofinite topology then infinite subset of $\mathbb{R}$ is?

Published on 16 Mar 2018 - 3:42

score 54 · Answer 4 · 2026-03-30 19:43:23

Find $f : [0,1] \to \mathbb R$ s.t. $\{x \in [0,1]$, for all neighborhood of $x$, there exist $y$ and $z$ in it s.t. $f(y)f(z)<0 \}\ $ is uncountable

score 637 · Answer 5 · 2026-03-25 11:48:03

637

Views

Induced Borel $\sigma$-algebra.

Published on 25 Mar 2026 - 11:48

score 48 · Answer 6 · 2018-03-16 14:17:25

48

Views

Is below set is open In $\mathbb{R^2}$

Published on 16 Mar 2018 - 14:17

score 59 · Answer 7 · 2026-03-31 14:03:45

59

Views

Uniqueness in Baire property representation for compact Hausdorff spaces

Published on 31 Mar 2026 - 14:03

score 631 · Answer 8 · 2026-03-27 06:30:07

631

Views

Quotient space and quotient map

Published on 27 Mar 2026 - 6:30

score 302 · Answer 9 · 2018-03-16 16:08:40

302

Views

"Inherits as a Subspace" in Toplogy

Published on 16 Mar 2018 - 16:08

score 277 · Answer 10 · 2026-03-24 23:54:04

277

Views

Continuity of a function from a one-point compactification to a cone

Published on 24 Mar 2026 - 23:54

score 33 · Answer 11 · 2018-03-16 18:35:51

33

Views

Imagining inside of complement set

Published on 16 Mar 2018 - 18:35

score 76 · Answer 12 · 2026-03-25 18:28:00

76

Views

Soft question - a subset of a Hilbert space endowed with subspace topology

Published on 25 Mar 2026 - 18:28

score 353 · Answer 13 · 2018-03-16 23:08:15

353

Views

Find the boundary and interior of $C= A \cup B$?

Published on 16 Mar 2018 - 23:08

score 1.8k · Answer 14 · 2018-03-17 02:15:11

1.8k

Views

The subset $[a, b)$ of $\Bbb R$ is neither open nor closed.

Published on 17 Mar 2018 - 2:15

score 592 · Answer 15 · 2018-03-17 03:21:13

592

Views

(Topology) In the real line $R^1$ a set is open if and only if it is a union of open segments (a,b).

Published on 17 Mar 2018 - 3:21

List Question

Unit ball in $l^{2}$ is bounded and closed but not compact.

Is $X$ a $T_1$ space? (i.e., given a pair of distinct points in $X$, does each one of them have a neighborhood not containing the other?)

Let $\mathbb{R}$ with cofinite topology then infinite subset of $\mathbb{R}$ is?

Find $f : [0,1] \to \mathbb R$ s.t. $\{x \in [0,1]$, for all neighborhood of $x$, there exist $y$ and $z$ in it s.t. $f(y)f(z)<0 \}\ $ is uncountable

Induced Borel $\sigma$-algebra.

Is below set is open In $\mathbb{R^2}$

Uniqueness in Baire property representation for compact Hausdorff spaces

Quotient space and quotient map

"Inherits as a Subspace" in Toplogy

Continuity of a function from a one-point compactification to a cone

Imagining inside of complement set

Soft question - a subset of a Hilbert space endowed with subspace topology

Find the boundary and interior of $C= A \cup B$?

The subset $[a, b)$ of $\Bbb R$ is neither open nor closed.

(Topology) In the real line $R^1$ a set is open if and only if it is a union of open segments (a,b).

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