On storage of topological information

• Published in: Discrete Applied Mathematics Vol. 147; no. 2; pp. 287 - 300
• Main Author: Kopperman, Ralph
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Lausanne Elsevier B.V 15.04.2005; Amsterdam Elsevier; New York, NY
• Subjects: [formula omitted]-space; Adjacency; Aleksandroff space; Algorithmics. Computability. Computer arithmetics; Applied sciences; Calming maps; Cartoon; Chaining maps; Computer science; control theory; systems; Connected ordered topological space (COTS); Digital k-space; Digital topology; Exact sciences and technology; General topology; Hausdorff reflection; Inverse limit; Jordan curve; Khalimsky line; Mathematics; Normalizing maps; Polyhedral analogs; Robust scene; Sciences and techniques of general use; Skew [formula omitted] compactness; Specialization (order); Theoretical computing; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds; Inverse limit; Jordan curve; Digital topology; Normalizing maps; Skew ( = stable ) compactness; Aleksandroff space; Digital k-space; Hausdorff reflection; Cartoon; Khalimsky line; T 0 -space; Specialization (order); Chaining maps; Robust scene; Polyhedral analogs; Calming maps; Connected ordered topological space (COTS); Adjacency; General topology; Compactness; Ordered space; Numerical approximation; Specialization; Euclidean space; Computer theory; Compact space; Skew (=stable) compactness; T0-space; Topological space; Information storage; Hausdorff space
• ISSN: 0166-218X; 1872-6771
• DOI: 10.1016/j.dam.2004.09.016

The usefulness of topology in science and mathematics means that topological spaces must be studied, and computers must be used in this study. Here are examples of this need from physics: In classical physics, the Euclidean spaces and compact Hausdorff spaces that arise can be approximated by finite spaces, and the goal of this paper is to discuss such approximation. A recent nonclassical development in physics uses a version of such finite approximation to view the universe as finite and eternally changing, and this is also discussed. Finite spaces are completely determined by their specialization orders. As a special case, digital n-space, used to interpret Euclidean n-space and in particular, the computer screen, is also dealt with in terms of the specialization.