On functional convergences. (English) Zbl 0606.54002

Pochcial, Jan

Rend. Ist. Mat. Univ. Trieste 17, 47-54 (1985).

Author’s summary: Starting with the research of conditions allowing a sequential convergence to be determined by a real-valued function, the introduction of two diagonal conditions leads to a characterization of quasi-normable spaces, like these of linear topologies. The main result is a source of new statements concerning metrizability and different kind of convergences.

Reviewer: B.Behrens

MSC:

54A20	Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
54D55	Sequential spaces
54E35	Metric spaces, metrizability

Keywords:

sequential convergence; diagonal conditions; quasi-normable spaces; metrizability