2024/02/17 by A. E. Lipin, Lipin, Anton
Computer Science · #Advanced Algebra and Logic #FOS: Mathematics #General Topology (math.GN)
paper · pdf · doi:10.48550/arxiv.2402.11213
openalex publication_date 2024/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate connections between resolvability and different forms of tightness. This study is adjacent to [1,2]. We construct a non-regular refinement τ^* of the natural topology of the real line ℝ with properties such that the space (ℝ, τ^*) has a hereditary nowhere dense tightness and it has no ω1-resolvable subspaces, whereas Δ(ℝ, τ^*) = \frakc. We also show that the proof of the main result of [1], being slightly modified, leads to the following strengthening: if L is a Hausdorff space of countable character and the space Lω is c.c.c., then every submaximal dense subspace of Lκ has disjoint tightness. As a corollary, for every κ≥ ω there is a Tychonoff submaximal space X such that |X|=Δ(X)=κ and X has disjoint tightness.