Abstract

Analysis Situs, or Topology, is the investigation of those properties of surfaces and spaces which are unaltered by deformation, that is, by bending and stretching without tearing. For example, a circular disc with a hole in it can be stretched so that its boundary circuits have any of a great variety of forms, but the number of circuits (two) remains unaltered—it is a topological invariant. The fundamental problem of topology (at present unsolved) is to determine necessary and sufficient conditions that a given surface or space A should be deformable into a given surface or space B.

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