A Short Study of Alexandroff Spaces

2007/08/16 by Timothy Speer, Speer, Timothy · 1 citation
Computer Science · Mathematics · #54-02 #Digital Image Processing Techniques #FOS: Mathematics #General Topology (math.GN) #Medical Image Segmentation Techniques #Topological and Geometric Data Analysis #math.GN #msc:54-02

paper · pdf · doi:10.48550/arxiv.0708.2136

10 pages

arxiv created 2007/08/16 · openalex publication_date 2007/08/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we discuss the basic properties of Alexandroff spaces. Several examples of Alexandroff spaces are given. We show how to construct new Alexandroff spaces from given ones. Finally, two invariants for compact Alexandroff spaces are defined and calculated for the given examples.

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• Homological framework of noncommutative complex analytic geometry and functional calculus

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