URYSOHN'S LEMMA IN SCHRÖDER CATEGORIES

概要

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A Schröder category extends the category of all binary relations among sets, that is, it realises a relatively huge part of predicate logic. On the other hand Urysohn's lemma asserts that every pair of disjoint closed subsets in a $T_4$ topological space can be separated by a continuous function into the reals. Usually the lemma is demonstrated with calculus of elementary set theory. However the structure of this lemma is very interesting from a view point of lattice theory and relational method. This paper gives a relational proof for Urysohn's lemma within Schröder categories.