On cohesive almost zero-dimensional spaces

DOI10.4153/S0008439520000545zbMATH Open1477.54031arXiv2002.07010MaRDI QIDQ5003444

Jan J. Dijkstra, David Sumner Lipham

Publication date: 22 July 2021

Published in: Canadian Mathematical Bulletin (Search for Journal in Brave)

Abstract: We investigate C-sets in almost zero-dimensional spaces, showing that closed $sigma$C-sets are C-sets. As corollaries, we prove that every rim-$sigma$-compact almost zero-dimensional space is zero-dimensional and that each cohesive almost zero-dimensional space is nowhere rational. To show these results are sharp, we construct a rim-discrete connected set with an explosion point. We also show every cohesive almost zero-dimensional subspace of $($Cantor set$)$$imesmathbbR$ is nowhere dense.

Full work available at URL: https://arxiv.org/abs/2002.07010

zbMATH Keywords

Lelek fanErdős spaceexplosion pointcohesive spacealmost zero-dimensional spaceone-point connectification.

Mathematics Subject Classification ID

Extensions of spaces (compactifications, supercompactifications, completions, etc.) (54D35) Topological spaces of dimension (leq 1); curves, dendrites (54F50) Dimension theory in general topology (54F45) Counterexamples in general topology (54G20)

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Related Items (6)

The zero-norm subspace of bounded cohomology ⋮ A dichotomy for spaces near dimension zero ⋮ Dispersion points and rational curves ⋮ Unnamed Item ⋮ A note on the topology of escaping endpoints ⋮ Unnamed Item

Uses Software

• MathOverflow

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