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Countable tightness is not discretely reflexive in -compact spaces
István Juhász, Jan van Mill
Answering a question raised by V. V. Tkachuk, we present several examples of -compact spaces, some only consistent and some in ZFC, that are not countably tight but in which the…
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…
Nowhere constant families of maps and resolvability
István Juhász, Jan van Mill
If is a topological space and is any set then we call a family of maps from to nowhere constant if for every non-empty open set in there is $f…
Homogeneous continuous images of smaller weight
István Juhász, Jan van Mill
We show that every infinite crowded space can be mapped onto a homogeneous space of countable weight, and that there is a homogeneous space of weight continuum that cannot be mappe…
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…
On the double density spectra of compact spaces
István Juhász, Jan Van Mill
The set of densities of all dense subspaces of a topological space is called the double density spectrum of . In this note we present a couple of results that imply…
Variations on countable tightness
István Juhász, Jan Van Mill
We consider 9 natural tightness conditions for topological spaces that are all variations on countable tightness and investigate the interrelationships between them. Several natura…