On the Existence of Categorical Universal Coverings

2011/11/29 by Ali Pakdaman, Pakdaman, Ali, Hamid Torabi +3 · 2 citations
Computer Science · #54D05 #55Q05 #57M10 #57M12 #Advanced Algebra and Logic #Algebraic Topology (math.AT) #FOS: Mathematics #General Topology (math.GN)

paper · pdf · doi:10.48550/arxiv.1111.6736

openalex publication_date 2011/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study necessary and sufficient conditions for the existence of categorical universal coverings using open covers of a given space X. As some applications, first we present a generalized version of the Shelah Theorem (Mycielski's conjecture: If X is a Peano continuum, then π₁(X,x) is uncountable or X has a simply connected universal covering) which states that a first countable Peano space has a categorical universal covering or has an uncountable fundamental group. Second, we prove that the one point union X₁\vee X₂=\fracX₁∪ X₂x₁∼ x₂ has a categorical universal covering if and only if both X₁ and X₂ have categorical universal coverings.

Cited by

• Comparison of Topologies on Fundamental Groups with Subgroup Topology Viewpoint
• On Subgroup Topologies on Fundamental Groups

Related

• Generalized Universal Covers of Uniform Spaces
• Universal covering spaces, a footnote
• Topological and uniform structures on universal covering spaces
• Coverings and fundamental groups: a new approach
• Partitions of unity and coverings