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b Indexed families of sets
8 other sections not shown
accumulation point arcwise connected Bdry borhood boundary called closed and bounded closed interval closed paths closed sets closed subset closure space Cmp(a compact space connected subset connected topological space connectedness contains an open continuous function continuous mapping Corollary correspondence cube Definition 2.3 denoted diagram distance function edges element Figure finite subcollection finite subcovering function defined function H Hausdorff space hence homeomorphic hood identification topology identification topology induced identify infinite subset intersection inverse functions Klein bottle Lemma Let F limn locally connected metric space neighborhood space non-empty obtain ological space one-one open covering open interval open sets open sphere open subset pair points xi positive integers Proof Prove real line real numbers rectangle relatively open sequence set containing set of points subset F subspace suppose terminal point Theorem 4.6 tion topological space union of sets X X Y xn+i xu x2