Topology, Volume 1

0-dimensional according arbitrary assume Axiom Baire property base belongs Borel set boundary set bounded called cartesian closed sets closure compact completely composed condition Consequently considered contains continuous function convergent COROLLARY countable defined definition denote dense dense set dimension disjoint distance domain easily elements equivalent example exists extension Finally finite follows formula Fr(X function function f Fund given Gj-set hand Hausdorff hence hold homeomorphism identity implies inclusion infinite Int(X intersection interval limit locally mapping Math means metric space Moreover Namely neighbourhood normal notion numbers obtain Obviously one-to-one open sets operation particular Proof propositional prove regular relation relative Remark replaced respectively satisfying scattered sense separable sequence subset Suppose THEOREM theory topological space topology true union whence