Journal of Computer Engineering and Informatics
Journal of Computer Engineering and Informatics(JCEI)

ISSN:23070072(Print)
ISSN:23070064(Online)

Frequency: Quarterly

Website: www.academicpub.org/jcei/


The Stone Theorem on Pairwise Paracompactness of Quasimetrizable Spaces 

Full Paper(PDF, 213KB) 


Abstract: 

The semantic values of programs or the data stored in a computer are usually rather discrete. Metrics can be used to study how these values relate to each other. In addition, we sometimes use a metric or generalizations of it to help us understand how discrete data stored inside a computer relate to the continuous real word. Paracompactness is an important topological property of metric spaces as it extends the benefits of finiteness to infinite sets. In this paper, A. H. Stone’s Theorem, that every metric space is paracompact, is extended to quasimetric spaces. Generally, inter alia, paracompactness in asymmetric topological spaces is related to locally finite topological spaces, which play an important role in digital topology and network science. 

Keywords:Quasipseudometrizable Space; Locally Finite (Spaces); Pairwise Paracompact 

Author: Athanasios Athanasios Andrikopoulos^{1}  1.Department of Economics, University of Ioannina, 26500 Ioannina, Greece 

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