Hereditary, continuous, homotopy, isotopy, productive and expansive topological properties

Abstract

Several separation axioms, connectedness and compactness as well as a number of other general topological properties are studied to determine whether or not they are invariant with respect to heredity, closed heredity, open heredity, continuity, open continuity, closed continuity, divisibility, retractions, projections, homotopy and isotopy equivalences, as well as finite, countable, and arbitrary products, and also with respect to contractions and expansions of the topology of a space. Of the resulting four hundred eighty questions, all but seven can be answered. The resulting answers, found and discussed in the paper, are also tabulated in several tables.