Sequentially complete spaces
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Roman Frič, Václav Koutník (1979)
Czechoslovak Mathematical Journal
Věra Trnková (1974)
Commentationes Mathematicae Universitatis Carolinae
Alessandro Caterino (1985)
Commentationes Mathematicae Universitatis Carolinae
Melvin Henriksen, Robert M. Raphael, Grant R. Woods (2007)
Commentationes Mathematicae Universitatis Carolinae
The set of isolated points (resp. -points) of a Tychonoff space is denoted by (resp. . Recall that is said to be scattered if whenever . If instead we require only that has nonempty interior whenever , we say that is SP-scattered. Many theorems about scattered spaces hold or have analogs for SP-scattered spaces. For example, the union of a locally finite collection of SP-scattered spaces is SP-scattered. Some known theorems about Lindelöf or paracompact scattered spaces hold also...
Constancio Hernández, Mihail G. Tkachenko (2004)
Commentationes Mathematicae Universitatis Carolinae
We show that every subgroup of an -factorizable abelian -group is topologically isomorphic to a closed subgroup of another -factorizable abelian -group. This implies that closed subgroups of -factorizable -groups are not necessarily -factorizable. We also prove that if a Hausdorff space of countable pseudocharacter is a continuous image of a product of -spaces and the space is pseudo--compact, then . In particular, direct products of -factorizable -groups are -factorizable and...
Constancio Hernández, Mihail G. Tkachenko (1998)
Commentationes Mathematicae Universitatis Carolinae
The properties of -factorizable groups and their subgroups are studied. We show that a locally compact group is -factorizable if and only if is -compact. It is proved that a subgroup of an -factorizable group is -factorizable if and only if is -embedded in . Therefore, a subgroup of an -factorizable group need not be -factorizable, and we present a method for constructing non--factorizable dense subgroups of a special class of -factorizable groups. Finally, we construct a closed...
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