Annali di Matematica Pura ed Applicata

, Volume 40, Issue 1, pp 211–221 | Cite as

Arrays of compact Pairs

  • D. G. Bourgin


The properties of direct limits ofCech homology groups for a non cofinal collection of compact pairs are explicitly stated with a view towards applications. The usual axioms including full excision are satisfied under obvious restrictions. Some of theMorse rank and span concepts are taken up in terms of these limit groups with the slight change of homology classes rather then cycles. A simple demonstration using the intuitive notions of the various cap types is presented for two basic exact sequences recently given byDeheuvel.


Exact Sequence Homology Group Limit Group Direct Limit Homology Class 
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  1. [D]
    R. Deheuvels,Topologie d'une fonctionelle, 61, pp. 13–72, 1955.zbMATHMathSciNetGoogle Scholar
  2. [M]
    M. Morse,Rank and Span in Functional/Topology, « Annals of Mathematics », 41, 419–454, 1940.CrossRefzbMATHMathSciNetGoogle Scholar
  3. [E. S.]
    S. Eilenberg-N. Steenrod,Foundations of Algebraic Topology, « Princeton Mathematical Series », 15.Google Scholar

Copyright information

© Swets & Zeitlinger B. V. 1955

Authors and Affiliations

  • D. G. Bourgin
    • 1
  1. 1.Urbana

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