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The Combinatory Method in Analysis Situs*

Published online by Cambridge University Press:  03 November 2016

M.H.A. Newman
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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.

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Type
Research Article
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The Mathematical Gazette , Volume 13 , Issue 185 , December 1926 , pp. 222 - 227
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.