2017/08/24 by Jintao Wang, Wang, Jintao · 1 citation
Mathematics · Medicine · #Advanced Topology and Set Theory #Algebraic Topology (math.AT) #Dual (grammatical number) #FOS: Mathematics #Hausdorff dimension #Hausdorff distance #Hausdorff measure #Hausdorff space #Homotopy #Homotopy and Cohomology in Algebraic Topology #Intracranial Aneurysms: Treatment and Complications #Mathematical analysis #Mathematics #Pure mathematics #Urysohn and completely Hausdorff spaces #math.AT
paper · pdf · doi:10.48550/arxiv.1708.07346
published in arXiv (Cornell University) (Cornell University) · 21 pages
openalex publication_date 2017/08/24 · arxiv created 2018/01/29 · arxiv updated 2018/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this paper, we aim to establish a new shape theory, compact Hausdorff shape (CH-shape) for general Hausdorff spaces. We use the "internal" method and direct system approach on the homotopy category of compact Hausdorff spaces. Such a construction can preserve most good properties of H-shape given by Rubin and Sanders. Most importantly, we can moreover develop the entire homology theory for CH-shape, including the exactness, dual to the consequence of Mardešić and Segal.