C-embedded Σ-spaces

σ-Normality of Topological Spaces

σ-normality of topological spaces

On Σ-countably Tight Spaces

Extending a result of R. de la Vega, we prove that an infinite homogeneous compactum has cardinality c if either it is the union of countably many dense or finitely many arbitrary countably tight subspaces. The question if every infinite homogeneous and σ-countably tight compactum has cardinality c remains open. We also show that if an arbitrary product is σ-countably tight then all but finitel...

On Σ-porous Sets in Abstract Spaces

The main aim of this survey paper is to give basic information about properties and applications of σ-porous sets in Banach spaces (and some other infinite-dimensional spaces). This paper can be considered a partial continuation of the author’s 1987 survey on porosity and σ-porosity and therefore only some results, remarks, and references (important for infinite-dimensional spaces) are repeated...

Some Screenable, Σ-relatively Discrete Dowker Spaces

Dowker spaces (that is, normal spaces that are not countably metacompact) are constructed which are also screenable and the countable union of discrete subspaces. The constructions and proofs are easy modifications of the ones for Balogh’s screenable Dowker space [B1]. Balogh’s example is presented alongside the modifications in a new exposition with several new results common to these spaces, ...