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Some references on point set topology:

May-Ponto: More concise algebraic topology (2012)

McCord: Classifying spaces and infinite symmetric products (1969)

Steenrod: A convenient category of topological spaces (1967)

Strickland: The category of CGWH spaces (notes, 2009)

Str?m: The homotopy category is a homotopy category (1972)