2007/03/25 by István Juhász, Istvan Juhasz, Juhasz, Istvan +5
Computer Science · Mathematics · #54A25 (Primary) #54A35 #54D20 #54D70 #54F05 (Secondary) #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #General Topology (math.GN) #Rings, Modules, and Algebras #math.GN #msc:54A25 #msc:54A35 #msc:54D20 #msc:54D70 #msc:54F05
paper · pdf · doi:10.48550/arxiv.math/0703728
arxiv created 2007/03/25 · openalex publication_date 2007/03/25 · arxiv updated 2009/12/01 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
We answer several questions of V. Tkačuk from [Point-countable π-bases in first countable and similar spaces, Fund. Math. 186 (2005), pp. 55--69.] by showing that (1) there is a ZFC example of a first countable, 0-dimensional Hausdorff space with no point-countable π-base (in fact, the order of any π-base of the space is at least ℵω); (2) if there is a κ-Suslin line then there is a first countable GO space of cardinality κ+ in which the order of any π-base is at least κ; (3) it is consistent to have a first countable, hereditarily Lindel" of regular space having uncountable π-weight and ω1 as a caliber (of course, such a space cannot have a point-countable π-base).