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Exchange of Limit and Integral with Nets

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#general-topology #measure-theory #nets
114
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Help me understand this passage from "General Topology" by J. Kelley

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#general-topology #nets
100
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Is there a way to see limits of nets as categorical limits?

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#category-theory #nets #limits-colimits
120
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Space as a network. Is it possible to model topological properties of Euclidean (or non-Euclidean) space using a discrete network of points?

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#geometric-topology #network #nets
701
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A bounded net with a unique limit point must be convergent

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#general-topology #limits #convergence-divergence #compactness #nets
177
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Ultralimit of an eventually constant generalized sequence

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#general-topology #limits #filters #nets
2k
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Closed graph implies $f$ continuous

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#general-topology #functional-analysis #continuity #nets #closed-graph
116
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Show that every subnet has a non-decreasing subnet

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#general-topology #nets
68
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Filters and their refinements vs nets and their subnets

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#general-topology #examples-counterexamples #filters #nets
333
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Advantages of viewing Cauchy Sequence criterion using directed set.

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#real-analysis #sequences-and-series #convergence-divergence #cauchy-sequences #nets
218
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Closed subset and function spaces

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#general-topology #nets
2k
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Where has this common generalization of nets and filters been written down?

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#general-topology #reference-request #convergence-divergence #filters #nets
1.1k
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Example of a subnet that have no subsequence.

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#general-topology #functional-analysis #examples-counterexamples #topological-vector-spaces #nets
403
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Use of directed sets in the definition of nets in topology

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#general-topology #limits #convergence-divergence #nets
618
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Cluster point vs limit point in net

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#general-topology #nets

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