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

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#real-analysis #general-topology #set-theory #ordinals #nets
76
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Kind of convergence theorem for nets

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#functional-analysis #convergence-divergence #lebesgue-integral #lebesgue-measure #nets
74
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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
#convergence-divergence #nets
170
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Does every net in $\mathbb{C}$ converging to $0$, have a countable subnet?

Published on
#convergence-divergence #nets
76
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Is a continuous net of hyperreal numbers eventually constant?

Published on
#real-analysis #general-topology #ordinals #nonstandard-analysis #nets
450
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A characterization for closed sets in topological vector spaces

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#weak-convergence #topological-vector-spaces #nets
54
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size issue related to universal quantifications over nets

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#general-topology #set-theory #nets
93
Views

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

Published on
#operator-theory #compact-operators #nets
91
Views

Nets and sequences in countable sets.

Published on
#sequences-and-series #general-topology #nets
233
Views

Proving diagonal principle for nets

Published on
#general-topology #convergence-divergence #nets
221
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Weak convergence iff all evaluated functionals converge

Published on
#functional-analysis #weak-convergence #nets #weak-topology
116
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Sequential properties of topological spaces

Published on
#general-topology #weak-convergence #nets
966
Views

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

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#general-topology #compactness #solution-verification #filters #nets
88
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Continuity of $F: X \times Y \to Z$ in terms of nets

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#general-topology #continuity #nets
39
Views

Characterising continuity of addition in a vector space with nets.

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#general-topology #vector-spaces #continuity #solution-verification #nets

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