Volume 2 Issue 3
Authors: Athanasios Athanasios Andrikopoulos
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 quasi-metric 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: Quasi-pseudometrizable Space; Locally Finite (Spaces); Pairwise Paracompact