Absolutely strongly star-Hurewicz 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.

Strongly k-spaces

‎In this paper‎, ‎we introduce the notion of strongly $k-$spaces (with the weak (=finest) pre-topology generated by their strongly compact subsets)‎. ‎We characterize the strongly $k-$spaces and investigate the relationships between preclosedness‎, ‎locally strongly compactness‎, ‎pre-first countableness and being strongly $k-$space.

HOMOTOPICAL EXCISION, AND HUREWICZ THEOREMS, FOR n-CUBES OF SPACES

where e is induced by the ‘excision’ inclusion. That e is an isomorphism in a range of dimensions is shown by the classical Blakers-Massey triad connectivity theorem: if A, B, and A∩B are connected, {A,B} is an open cover of X and (A, A ∩ B) is p-connected, (B, A ∩ B) is q-connected, then the triad (X; A,B) is (p + q)-connected. (See, for example, [11, p. 211].) Further, if p, q > 2 and π1(A∩B)...

Non-absolutely Convergent Integrals in Metric Spaces

Absolutely convex sets in barrelled spaces

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