A dichotomy for spaces near dimension zero

Abstract

We prove that the classes of weakly $1$-dimensional and almost $0$-dimensional spaces are disjoint. The result has applications to hereditarily locally connected spaces, $\mathbb{R}$-trees, and endpoints of smooth fans.

References in corpus (3)

• Cosmic dimensions
• On cohesive almost zero-dimensional spaces
• Fences, their endpoints, and projective Fraïssé theory

Cited by in corpus (1)

• Buried points of plane continua