List questions from nets

Published on 13 May 2021 - 3:49

39

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Is there a basis for sequences?

Published on 14 May 2021 - 13:31

407

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To prove: if X' is not compact, then there is a countably infinite discrete set in X.

Published on 18 May 2021 - 5:10

37

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Non-dense subspace implies non-zero measure

Published on 26 May 2021 - 10:17

73

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sequence with an accumaltion point, but no converging subsequence

Published on 01 Jun 2021 - 13:50

61

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can one speak of $\max(i,j)$ for elements $i,j$ of a directed set?

Published on 06 Jun 2021 - 4:46

86

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Continuous function and net (Solution Verification)

Published on 21 Jun 2021 - 5:21

65

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Convergence of net in $C^\infty(0,\infty)$ implies pointwise convergence.

Published on 26 Feb 2026 - 1:20

118

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Convergence of product of two convergent nets in a topological group.

Published on 26 Jun 2021 - 7:53

38

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On Tichonoff's theorem and convergent subnets

Published on 30 Jun 2021 - 14:17

35

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Limit set of a net in $(\mathbb R, T_{CF})$

Published on 03 Jul 2021 - 23:08

101

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If $\sum_{s \in S} \|h_s\| < \infty$ then $\sum_{s \in S} h_s$ converges.

Published on 06 Jul 2021 - 18:54

71

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$K\subseteq X$ is compact iff every net in $K$ has an accumulation point in $K$

Published on 09 Jul 2021 - 0:48

29

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Exercise about convergence of a net in $(\mathbb R, T_{CF})$

Published on 14 Jul 2021 - 22:13

43

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Routine verification of net convergence

Published on 25 Jul 2021 - 21:03

List Question

Weak vs. Weak* Convergence of Bounded Nets

Is there a basis for sequences?

To prove: if X' is not compact, then there is a countably infinite discrete set in X.

Non-dense subspace implies non-zero measure

sequence with an accumaltion point, but no converging subsequence

can one speak of $\max(i,j)$ for elements $i,j$ of a directed set?

Continuous function and net (Solution Verification)

Convergence of net in $C^\infty(0,\infty)$ implies pointwise convergence.

Convergence of product of two convergent nets in a topological group.

On Tichonoff's theorem and convergent subnets

Limit set of a net in $(\mathbb R, T_{CF})$

If $\sum_{s \in S} \|h_s\| < \infty$ then $\sum_{s \in S} h_s$ converges.

$K\subseteq X$ is compact iff every net in $K$ has an accumulation point in $K$

Exercise about convergence of a net in $(\mathbb R, T_{CF})$

Routine verification of net convergence

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