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The Combinatory Method in Analysis Situs*

Published online by Cambridge University Press:  03 November 2016

Extract

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.

Type
Research Article
Copyright
Copyright © Mathematical Association 1926

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Footnotes

page 222 note *

Read at the British Association Meeting, Oxford, 1926.

References

page 224 note * The next few paragraphs give the general idea of the Heegaard-Dehn system, but the details are different at a number of points.

page 224 note † More accurately, the third 1-set must be congruent to sets obtainable by internal transformations from the other two. Two sets are congruent if they can be specified by the same scheme.

page 224 note ‡ These definitions should, of course, be “realised” with the help of a figure.

page 226 note * More accurately into an array congruent to Δ. Cf. footnote, p. 224.