# On $\sigma$-countably tight spaces

Authors
Type
Preprint
Publication Date
Jul 02, 2016
Submission Date
Jul 02, 2016
Identifiers
arXiv ID: 1607.00517
Source
arXiv
Extending a result of R. de la Vega, we prove that an infinite homogeneous compactum has cardinality $\mathfrak{c}$ if either it is the union of countably many dense or finitely many arbitrary countably tight subspaces. The question if every infinite homogeneous and $\sigma$-countably tight compactum has cardinality $\mathfrak{c}$ remains open. We also show that if an arbitrary product is $\sigma$-countably tight then all but finitely many of its factors must be countably tight.