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Foreword to the first English edition
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algebra arbitrary assign assumption axiom belong boundary set called cartesian product chain complex Chapter XII closed interval closed sets closed subset Cn(K coefficients compact space completely regular component connected sets contains continuous function continuous mapping convergent Corollary countable base deduce defined definition denote dense dimensional disjoint elements equivalence example Exercise exists finite number following theorem formula functor given hence Hilbert cube Hn(K homology groups homomorphism homotopic implies inequality infinite sequence initial interval intersection Lemma Let us assume locally connected space metric space morphism natural numbers non-empty one-to-one open cover open sets order type ordered set ordinal numbers orientation pair Proof propositional function rational numbers real numbers Remark satisfies conditions set theory simplex simplicial complex simplicial map topological space topology uniform convergence union variables vertex virtue of Theorem