H-enrichments of Topologies
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General Topology and Its Applications
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An H-enrichment of a topology on a set X is a topology on X such that and every homeomorphism from X to itself with respect to is also a homeomorphism with respect to . An H-enrichment is a C-enrichment if “homeomorphism” can be replaced by “continuous function” above. Generally in “nice” spaces, there is a scarcity of C-enrichments and an abundance of H-enrichments. We capitalize on the scarcity of C-enrichments to prove classification theorems for minimally free rings of continuous real-valued functions; with H-enrichments in general, we focus on separation and connectedness axioms.