Titlebook: Essential Topology; Martin D. Crossley Textbook 2005 Springer-Verlag London Limited 2005 Algebraic topology.Continuity.Fundamental group.H

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Marc Fetscherin,Tobias Heilmanne spaces cannot be expressed in such a way, and even those that can, can usually be expressed as a simplicial complex in many different ways. Choosing one way can obscure some details of the space. For these reasons “singular” homology was developed, which gets around this problem by, in a very loos

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John M. Barron,Michael E. StatenSo far, we have only considered functions on the real line. We have seen how to hide those annoying ?s and δs in the definition of continuity, replacing them with open sets. This enables us to consider functions with domains and ranges different from R; all we need is some notion of “open set”.

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Continuous Functions,As topology is essentially just the study of continuous functions, we should start by clarifying exactly what we mean by the word “continuous”. We will begin by considering the most familiar type of function, namely those which are defined for some (or all) real numbers, and which return a real number