2025/05/24 by A. V. Lipin, Lipin, Anton · 1 citation
Computer Science · #Advanced Algebra and Logic #FOS: Mathematics #General Topology (math.GN)
paper · pdf · doi:10.48550/arxiv.2505.18704
openalex publication_date 2025/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Suppose X and Y are topological spaces, |X| = Δ(X) and |Y| = Δ(Y). We investigate resolvability of the product X × Y. We prove that: I. If |X| = |Y| = ω and X,Y are Hausdorff, then X × Y is maximally resolvable; II. If 2κ= κ+, \|X|, cf|X|\ ∩ \κ, κ+\ ≠ ∅ and cf|Y| = κ+, then the space X × Y is κ+-resolvable. In particular, under GCH the space X2 is cf|X|-resolvable whenever cf|X| is an isolated cardinal; III. (\frakr = \frakc) If cf|X| = ω and cf|Y| = cf(\frakc), then the space X × Y is ω-resolvable. If, moreover, cf(\frakc) = ω1, then the space X × Y is ω1-resolvable.