List questions from compactness

Published on 24 Mar 2026 - 22:11

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If $A$ is closed and $B$ is compact, prove $A\cap B$ is compact

Published on 26 Feb 2018 - 17:27

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Let $Q$ be the set of all $x \in H$ of the form $x = \sum_1^{\infty} c_n u_n$ for $|c_n| \le \frac 1n$. Show that $Q$ is compact.

Published on 27 Feb 2018 - 13:59

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About the proof: $\mathbb Q$ is not locally compact

Published on 27 Feb 2018 - 19:46

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Show that $(X,d)$ is compact

Published on 24 Mar 2026 - 4:02

176

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Find the connected component of 1/2 in [0, 1], and say if [0,1] is compact for these topologies

Published on 25 Mar 2026 - 13:34

87

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Showing compactness and precompactness

Published on 01 Mar 2018 - 2:32

79

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Is K := {$\frac{1}{n+1}$| n ∈ N} compact on $T_{up}$, $T_{k}$ and $T_{uplim}$?

Published on 01 Mar 2018 - 4:49

46

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Under what conditions on the sequence {$a_n$}, $a_n>0$, the following set is compact in $l^2$

Published on 01 Mar 2018 - 6:38

38

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Is [0,1] compact in $T_{up}$?

Published on 01 Mar 2018 - 17:40

110

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precompactness of integral of functions in $C^1[a,b]$

Published on 01 Mar 2018 - 18:35

95

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Is $K:=\{\frac{1}{n}\mid n \in N\} \cup \{0\} $ compact in $T_{st}$?

Published on 01 Mar 2018 - 22:03

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Give an example of a topology that is not compact, not connected, and not Hausdorff

Published on 25 Mar 2026 - 13:34

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Compactness of [1,2] and [1,2).

Published on 02 Mar 2018 - 10:21

339

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Compact,connected set

Published on 26 Mar 2026 - 19:50

List Question

Example of an unbounded $w^*-$ compact subset

If $A$ is closed and $B$ is compact, prove $A\cap B$ is compact

Let $Q$ be the set of all $x \in H$ of the form $x = \sum_1^{\infty} c_n u_n$ for $|c_n| \le \frac 1n$. Show that $Q$ is compact.

About the proof: $\mathbb Q$ is not locally compact

Show that $(X,d)$ is compact

Find the connected component of 1/2 in [0, 1], and say if [0,1] is compact for these topologies

Showing compactness and precompactness

Is K := {$\frac{1}{n+1}$| n ∈ N} compact on $T_{up}$, $T_{k}$ and $T_{uplim}$?

Under what conditions on the sequence {$a_n$}, $a_n>0$, the following set is compact in $l^2$

Is [0,1] compact in $T_{up}$?

precompactness of integral of functions in $C^1[a,b]$

Is $K:=\{\frac{1}{n}\mid n \in N\} \cup \{0\} $ compact in $T_{st}$?

Give an example of a topology that is not compact, not connected, and not Hausdorff

Compactness of [1,2] and [1,2).

Compact,connected set

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