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Sequential definitions of compactness. (English) Zbl 1145.54001
Let \(X\) be a topological group and \(G\) an additive function from a subgroup of the group of sequences in \(X\) into \(X\); unifying matrix summability, Banach limit, summability in topological groups, statistical convergence and others, the author calls a sequence \(x_n\) \(G\)-convergent to \(x\) if \(x= G(x_n)\), introduces \(G\)-sequential versions of closedness, compactness and continuity and studies relations between these concepts.

MSC:
54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
43A55 Summability methods on groups, semigroups, etc.
54D30 Compactness
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