Decision algorithms for elementary topology I. Topological syllogistics with set and map constructs, connectedness, and cardinality comparison

In this paper we give a decision procedure for a topological syllogistic, denoted ℒ2,∞, 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.