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Results tagged with nets
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user 128226
A net is a generalization of a sequence where a directed set is used as the index set instead of positive integers. Convergence of nets can be defined in a similar way as convergence of sequences. Convergent nets in a topological space uniquely determine its topology.
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Quantification over Nets
On a topological space $X$, a net is defined as a map $A \ni \alpha \longmapsto x_{\alpha} \in X$ from a directed set $A$.
With this, compactness of $X$ (for instance) is equivalent to "every net $(x …
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