Media type: E-Article Title: Decision algorithms for elementary topology I. Topological syllogistics with set and map constructs, connectedness, and cardinality comparison Contributor: Cantone, Domenico; Cutello, Vincenzo imprint: Wiley, 1994 Published in: Communications on Pure and Applied Mathematics Language: English DOI: 10.1002/cpa.3160470903 ISSN: 0010-3640; 1097-0312 Keywords: Applied Mathematics ; General Mathematics Origination: Footnote: Description: <jats:title>Abstract</jats:title><jats:p>In this paper we give a decision procedure for a topological syllogistic, denoted ℒ<jats:sup>2</jats:sup>,∞, involving, besides the standard Boolean set operators (∩, ∩, ′ (set complementation)) and predicates ( ϵ (membership), = (equality)), also the Kuratowski closure operator, continuous and closed maps with the notion of direct and inverse images, surjectivity and injectivity, as well as point evaluation, the singleton operator {·}, a predicate for comparing the cardinalities of two given sets, and a predicate expressing that a given set is topologically connected. Several examples are also discussed. © 1994 John Wiley & Sons, Inc.</jats:p>