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Incidence Relations in MulticoherentSpaces II

Published online by Cambridge University Press:  20 November 2018

A. H. Stone
A. H. Stone*
Affiliation:
Manchester University
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Introduction. One standard method of studying the incidences of a system of sets A 1, A2, .… , An is to consider the nerve of the system. However, this gives no direct information as to the numbers of components of the various intersections of the sets—information which would be desirable in several geometrical problems. The object of the present paper is to modify the definition of the nerve so that these numbers of components can be taken into account, and to study this modified nerve for systems of sets in a connected, locally connected, normal T1 space S of a given degree of multicoherence r(S). The principal result (Theorem 6, 6.4) is a refinement of a theorem of Eilenberg [4, p. 107], and asserts that, if then under suitable hypotheses we have

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Type
Research Article
Information
Canadian Journal of Mathematics , Volume 2 , 1950 , pp. 461 - 480
Copyright
Copyright © Canadian Mathematical Society 1950

References

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