
We give some necessary and sufficient conditions for the character of spaces to be preserved under closed maps.
Noncompact covering properties (paracompact, Lindelöf, etc.), Special maps on topological spaces (open, closed, perfect, etc.), GCH, alpha-compact space, ZFC, countable tightness, strongly collectionwise Hausdorff space, Sequential spaces, MA, Cardinality properties (cardinal functions and inequalities, discrete subsets), boundaries, alpha-Lindelöf space
Noncompact covering properties (paracompact, Lindelöf, etc.), Special maps on topological spaces (open, closed, perfect, etc.), GCH, alpha-compact space, ZFC, countable tightness, strongly collectionwise Hausdorff space, Sequential spaces, MA, Cardinality properties (cardinal functions and inequalities, discrete subsets), boundaries, alpha-Lindelöf space
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