On zero dimensional sequential spaces

2020/07/04 by Paul Fabel, Fabel, Paul
Mathematics · #54B15 (Primary) 54D55 54F45 55M10(Secondary) #Advanced Topology and Set Theory #Artificial intelligence #Combinatorics #Computer science #Dimension (graph theory) #Embedding #FOS: Mathematics #General Topology (math.GN) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematics #Pure mathematics #Quotient #Space (punctuation) #Topological space #Topological vector space #Topology (electrical circuits) #Zero (linguistics) #Zero-dimensional space #math.GN #msc:54B15 #msc:54D55 #msc:54F45

paper · pdf · doi:10.48550/arxiv.2007.02136

published in arXiv (Cornell University) (Cornell University) · 20 pages

arxiv created 2020/07/04 · openalex publication_date 2020/07/04 · arxiv updated 2020/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/08

Abstract

We develop tools to recognize sequential spaces with large inductive dimension zero. We show the Hawaiian earring group G is 0 dimensional, when endowed with the quotient topology, inherited from the space of based loops with the compact open topology. In particular G is T₄ and hence inclusion G → F_M (G) is a topological embedding into the free topological group F_M (G) in the sense of Markov.

Citations

• Monoidal closed, Cartesian closed and convenient categories of topological spaces

Related

• The Hawaiian earring group and metrizability
• Multiplication is discontinuous in the Hawaiian earring group (with the quotient topology)
• The Hawaiian earring group is topologically incomplete
• Making spaces wild (simply-connected case)
• The Topological Fundamental Group and Hoop Earring Spaces