Nest and Complete Accumulation Point Compactness ot the Product of Topological Spaces

Abstract

Based on the definition of nest compactness (Ie., the intersection of a nest of nonempty closed sets is nonempty) we show that the product of the two nest compáct topological spaces is nest compact, and, this without invoking the compactness of the product of two compact topological spaces based on the classical definition of compactness (i.e., every open cover has a finit subcover). The same is done based on the definition of complete accumulation point compactness. The latter, by Remark 5, extends easily to the infinite products of topological spaces.