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Examples of sequential topological groups under the continuum hypothesis

Alexander Shibakov (1996)

Fundamenta Mathematicae

Using CH we construct examples of sequential topological groups: 1. a pair of countable Fréchet topological groups whose product is sequential but is not Fréchet, 2. a countable Fréchet and α 1 topological group which contains no copy of the rationals.

Extension of multisequences and countably uniradial classes of topologies

Szymon Dolecki, Andrzej Starosolski, Stephen W. Watson (2003)

Commentationes Mathematicae Universitatis Carolinae

It is proved that every non trivial continuous map between the sets of extremal elements of monotone sequential cascades can be continuously extended to some subcascades. This implies a result of Franklin and Rajagopalan that an Arens space cannot be continuously non trivially mapped to an Arens space of higher rank. As an application, it is proved that if for a filter on ω , the class of -radial topologies contains each sequential topology, then it includes the class of subsequential topologies....

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