Question

Proof that a closed subset of a compact space is a compact space

score 101 · Answer 1 · 2019-06-02 12:38:22

101

Views

Proof that a closed subset of a compact space is a compact space

Published on 02 Jun 2019 - 12:38

score 36 · Answer 2 · 2019-06-03 08:57:33

36

Views

Relatively compact set theorem from Billingsley's Convergence of Probability Measure

Published on 03 Jun 2019 - 8:57

score 115 · Answer 3 · 2019-06-04 15:55:23

115

Views

Conclude $\left\|f_n-f\right\|_\infty\to0$ from knowing that $f_n(x_n)\to f(x)$ for all $(x_n)$ and $x$

Published on 04 Jun 2019 - 15:55

score 79 · Answer 4 · 2026-03-26 06:26:15

79

Views

Non-constant analytic function on a compact set

Published on 26 Mar 2026 - 6:26

score 74 · Answer 5 · 2019-06-06 02:49:53

74

Views

Which of the following statements are true?(NBHM-2016,Topology(3.7))

Published on 06 Jun 2019 - 2:49

score 55 · Answer 6 · 2026-03-27 18:11:08

55

Views

Prove: $(\forall \epsilon > 0 )(\forall x \in K)(\exists U \in O(x))(\forall f \in Z)(\forall y \in U) | f(x) - f(y) | < \epsilon$ .

Published on 27 Mar 2026 - 18:11

score 522 · Answer 7 · 2026-03-23 03:03:48

522

Views

Characteristic of a connected, locally compact, Hausdorff space X which is locally connected.

Published on 23 Mar 2026 - 3:03

score 212 · Answer 8 · 2019-06-07 12:51:48

212

Views

Compact nested subsets

Published on 07 Jun 2019 - 12:51

score 1.2k · Answer 9 · 2019-06-07 18:42:05

1.2k

Views

Infinite product is not locally compact.

Published on 07 Jun 2019 - 18:42

score 77 · Answer 10 · 2019-06-08 20:58:58

77

Views

Characterization of compact metrics spaces

Published on 08 Jun 2019 - 20:58

score 131 · Answer 11 · 2026-03-26 03:12:37

131

Views

Prove that $A$ is a compact subset of $M_3(\Bbb R) \cong \Bbb R^9$.

Published on 26 Mar 2026 - 3:12

score 408 · Answer 12 · 2026-03-26 08:00:39

408

Views

Probs. 3 (a & c), Sec. 27, in Munkres' TOPOLOGY, 2nd ed: The space $\mathbb{R}_K$ is not path connected and $[0, 1]$ is not compact in $\mathbb{R}_K$.

Published on 26 Mar 2026 - 8:00

score 103 · Answer 13 · 2019-06-11 14:08:58

103

Views

a question for arbitrary union of compact sets

Published on 11 Jun 2019 - 14:08

score 908 · Answer 14 · 2026-03-26 04:53:36

908

Views

Prob. 6, Sec. 27, in Munkres' TOPOLOGY, 2nd ed: The Cantor's set is totally disconnected, compact, and uncountable

Published on 26 Mar 2026 - 4:53

score 1.6k · Answer 15 · 2019-06-12 10:42:34

1.6k

Views

The set $\Omega \subset \mathbb{C}$ is compact iff every sequence $\{ z_n \} \subset \Omega$ has a subsequence that converges to a point in $\Omega$

Published on 12 Jun 2019 - 10:42

List Question

Proof that a closed subset of a compact space is a compact space

Relatively compact set theorem from Billingsley's Convergence of Probability Measure

Conclude $\left\|f_n-f\right\|_\infty\to0$ from knowing that $f_n(x_n)\to f(x)$ for all $(x_n)$ and $x$

Non-constant analytic function on a compact set

Which of the following statements are true?(NBHM-2016,Topology(3.7))

Prove: $(\forall \epsilon > 0 )(\forall x \in K)(\exists U \in O(x))(\forall f \in Z)(\forall y \in U) | f(x) - f(y) | < \epsilon$ .

Characteristic of a connected, locally compact, Hausdorff space X which is locally connected.

Compact nested subsets

Infinite product is not locally compact.

Characterization of compact metrics spaces

Prove that $A$ is a compact subset of $M_3(\Bbb R) \cong \Bbb R^9$.

Probs. 3 (a & c), Sec. 27, in Munkres' TOPOLOGY, 2nd ed: The space $\mathbb{R}_K$ is not path connected and $[0, 1]$ is not compact in $\mathbb{R}_K$.

a question for arbitrary union of compact sets

Prob. 6, Sec. 27, in Munkres' TOPOLOGY, 2nd ed: The Cantor's set is totally disconnected, compact, and uncountable

The set $\Omega \subset \mathbb{C}$ is compact iff every sequence $\{ z_n \} \subset \Omega$ has a subsequence that converges to a point in $\Omega$

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