Topology

Abstract

In the present essay, we attempt to convey some idea of the skeleton of topology, and of various topological concepts. It must be said at once that, apart from the necessary minimum, the subject-matter of this survey does not include that subdiscipline known as “general topology ” — the theory of general spaces and maps considered in the context of set theory and general category theory. (Doubtless this subject will be surveyed in detail by others.) With this qualification, it may be claimed that the “topology ” dealt with in the present survey is that mathematical subject which in the late 19th century was called Analysis Situs, and at various later periods separated out into various subdisciplines: “Combinatorial topology ”, “Algebraic topology ”, “Differential (or smooth) topology ”, “Homotopy theory ”, “Geometric topology ”.