List questions from nets

Published on 22 Mar 2026 - 11:32

75

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Kind of convergence theorem for nets

Published on 09 Nov 2019 - 16:20

73

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$(x_t)_{t\in\Lambda}$ is a bounded net in $\mathbb{C}$ that doesn't converge to $0$. Does it have a subnet that is outside of a $B(0,\epsilon)$?

Published on 22 Nov 2019 - 17:00

169

Views

Does every net in $\mathbb{C}$ converging to $0$, have a countable subnet?

Published on 24 Nov 2019 - 8:41

75

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Is a continuous net of hyperreal numbers eventually constant?

Published on 27 Nov 2019 - 21:59

449

Views

A characterization for closed sets in topological vector spaces

Published on 28 Nov 2019 - 20:52

53

Views

size issue related to universal quantifications over nets

Published on 04 Dec 2019 - 3:59

92

Views

Bounded operator and image of convergent net is compact implies compact operator

Published on 11 Dec 2019 - 10:30

90

Views

Nets and sequences in countable sets.

Published on 17 Dec 2019 - 12:44

232

Views

Proving diagonal principle for nets

Published on 15 Jan 2020 - 18:07

220

Views

Weak convergence iff all evaluated functionals converge

Published on 16 Jan 2020 - 20:16

115

Views

Sequential properties of topological spaces

Published on 12 Feb 2020 - 7:02

965

Views

$X$ is compact iff every net in $X$ has a convergent subnet (using filters).

Published on 14 Feb 2020 - 10:49

87

Views

Continuity of $F: X \times Y \to Z$ in terms of nets

Published on 14 Feb 2020 - 14:52

38

Views

Characterising continuity of addition in a vector space with nets.

Published on 16 Feb 2020 - 20:58

List Question

Is the limit of a recursively defined ordinal-indexed sequence always a fixed point?

Kind of convergence theorem for nets

$(x_t)_{t\in\Lambda}$ is a bounded net in $\mathbb{C}$ that doesn't converge to $0$. Does it have a subnet that is outside of a $B(0,\epsilon)$?

Does every net in $\mathbb{C}$ converging to $0$, have a countable subnet?

Is a continuous net of hyperreal numbers eventually constant?

A characterization for closed sets in topological vector spaces

size issue related to universal quantifications over nets

Bounded operator and image of convergent net is compact implies compact operator

Nets and sequences in countable sets.

Proving diagonal principle for nets

Weak convergence iff all evaluated functionals converge

Sequential properties of topological spaces

$X$ is compact iff every net in $X$ has a convergent subnet (using filters).

Continuity of $F: X \times Y \to Z$ in terms of nets

Characterising continuity of addition in a vector space with nets.

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