WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 23, 2024
Applications of Locally Compact Spaces in Polyhedra: Dimension and Limits
Authors: , ,
Abstract: The study of applications of locally compact spaces in polyhedra in relation to their dimensions as well as homotopy and extension problems developed in the late 1940s and early 1950s under the leadership of mathematician. Many mathematicians studied application locally compact in polyhedra. A polyhedron can be obtained by subdivision, as a simplicial metric complex; thus, re-gluings of polyhedra can also be seen as simple complexes. Thus, the topology of a simplicial metric complex X is the topology quotient of the reattachment. The objective of this work is to shed light on the applications in polyhedra of locally compact spaces and to highlight the limits of these applications. A continuous application f of X in P defines a finite open overlay of X, and a partition of the unit subordinate to this overlay, f is homotopic to an application f ', obtained by composing the restriction to A, of an application of X in the KR polyhedron, and a simplistic application of a sub-polyhedron KR' in P. The problem of extension deserves to be elucidated to understand how it is possible to get around certain conceptual difficulties.
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Keywords: polyhedron, compact spaces, locally compact spaces, paracompact spaces, CECH COHOMOLOGY, homotopy, extension
Pages: 118-124
DOI: 10.37394/23206.2024.23.14