DECISION ALGORITHMS FOR ELEMENTARY TOPOLOGY .1. TOPOLOGICAL SYLLOGISTICS WITH SET AND MAP CONSTRUCTS, CONNECTEDNESS, AND CARDINALITY COMPARISON

In this paper we give a decision procedure for a topological syllogist ic, denoted L2,infinity, involving, besides the standard Boolean set o perators (or, and, \, ' (set complementation)) and predicates (is-an-e lement-of (membership), = (equality)), also the Kuratowski closure ope rator , continuous and closed maps with the notion of direct and inver se images, surjectivity and injectivity, as well as point evaluation, the singleton operator {.}, a predicate for comparing the cardinalitie s of two given sets, and a predicate expressing that a given set is to pologically connected. Several examples are also discussed. (C) 1994 J ohn Wiley & Sons, Inc.