Increasing chains and discrete reflection of cardinality

2015/05/22 by Santi Spadaro, Spadaro, Santi
Mathematics · #FOS: Mathematics #General Topology (math.GN) #Graph theory and applications #math.GN

paper · pdf · doi:10.48550/arxiv.1505.06251

arxiv created 2015/05/22 · openalex publication_date 2015/05/22 · arxiv updated 2015/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

Combining ideas from two of our previous papers, we refine Arhangel'skii Theorem by proving a cardinal inequality of which this is a special case: any increasing union of strongly discretely Lindelof spaces with countable free sequences and countable pseudocharacter has cardinality at most continuum. We then give a partial positive answer to a problem of Alan Dow on reflection of cardinality by closures of discrete sets.

Citations

• Infinite games and cardinal properties of topological spaces

Related

• On the cardinality of almost discretely Lindelof spaces
• Strong dichotomy of cardinality
• On closures of discrete sets
• Lindelof indestructibility, topological games and selection principles
• First countable and almost discretely Lindelöf T₃ spaces have cardinality at most continuum