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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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##### References:
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