Absolutely Closed Spaces

Closed subsets of absolutely star-Lindelöf spaces II

In this paper, we prove the following two statements: (1) There exists a discretely absolutely star-Lindelöf Tychonoff space having a regular-closed subspace which is not CCC-Lindelöf. (2) Every Hausdorff (regular, Tychonoff) linked-Lindelöf space can be represented in a Hausdorff (regular, Tychonoff) absolutely star-Lindelöf space as a closed Gδ subspace.

Absolutely Closed Nil-2 Groups

Using the description of dominions in the variety of nilpotent groups of class at most two, we give a characterization of which groups are absolutely closed in this variety. We use the general result to derive an easier characterization for some subclasses; e.g. an abelian group G is absolutely closed in N2 if and only if G/pG is cyclic for every prime number p . The main result of this paper i...

Non-absolutely Convergent Integrals in Metric Spaces

Absolutely convex sets in barrelled spaces

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Generalized Closed Sets in Čech Closed Spaces

The purpose of the present paper is to introduce the concept of generalized closed sets in Čech closure spaces and investigate some of their characterizations. 2000 Mathematics Subject Classification: 54A05.