6 papers
Noetherian Properties, Large Cardinals, and Independence Around
Lajos Soukup, Zoltán Szentmiklóssy
A base of a topological space is called {\em Noetherian } iff it does not contain an infinite strictly -increasing chain. We show that minimal cardinality of a regular s…
Some new results on -spaces
I. Juhász, J. van Mill, L. Soukup +1
A topological space is a -space (or ) if for any decreasing sequence of subsets of with empty intersection there is a (decreasing) sequence $\…
Selectively pseudocompact spaces
István Juhász, Lajos Soukup, Zoltán Szentmiklóssy
A novel selection principle was introduced by Dorantes-Aldama and Shakhmatov: a topological space is termed {\em selectively pseudocompact} if for any sequence o…
On the companion of spaces having dense, relatively countable compact subspaces
István Juhász, Lajos Soukup, Zoltán Szentmiklóssy
The notion of "pseudocompactness" was introduced by Hewitt. The concept of relatively countably compact subspaces were explored by Marjanovic to show that a -space is pseudocomp…
Pseudocompact versus countably compact in first countable spaces
István Juhász, Ljos Soukup, Zoltán Szentmiklóssy
The primary objective of this work is to construct spaces that are "pseudocompact but not countably compact," abbreviated as PNC, while endowing them with additional properties. Fi…
The class and countable net weight
István Juhász, Lajos Soukup, Zoltán Szentmiklóssy
Hart and Kunen, and independently in the recent preprint arXiv:2304.13113, Ríos-Herrejón defined and studied the class of topological spaces having the property that f…