On resolvability, connectedness and pseudocompactness

2023/08/02 by Lipin, Anton
#FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.2308.01259

Abstract

We prove that: I. If L is a T₁ space, |L|>1 and d(L) ≤ κ≥ ω, then there is a submaximal dense subspace X of L^2κ such that |X|=Δ(X)=κ; II. If \frakc≤κ=κ^ω<λ and 2^κ=2^λ, then there is a Tychonoff pseudocompact globally and locally connected space X such that |X|=Δ(X)=λ and X is not κ⁺-resolvable; III. If ω₁≤κ<λ and 2^κ=2^λ, then there is a regular space X such that |X|=Δ(X)=λ, all continuous real-valued functions on X are constant (so X is pseudocompact and connected) and X is not κ⁺-resolvable.

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