The topological properties under the definition of topologically preserving mappings are discussed.And it is obtained that topologically preserving mappings are homeomorphisms under the assumption of T0 separation axiom.Moreover,some cardinality invariants under topologically pre-serving mappings,are dicussed and it is obtained that the connectivity,compactness,paracompact-ness,countable compactness are preserved by topologically preserving mappings.
topology preserving mappingopen mappingclosed mappingdensityseparable spaceparacompact space
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