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Relative simplicial approximation

Published online by Cambridge University Press:  24 October 2008

E. C. Zeeman
E. C. Zeeman
Affiliation:
Gonville and Caius College, Cambridge
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Extract

The absolute simplicial approximation theorem, which dates back to Alexander (l), states that there is a simplicial approximation g to any given continuous map f between two finite simplicial complexes (see for instance (2), p. 37 or (3), p. 86). The relative theorem given here permits us to leave f unchanged on any subcomplex, on which f happens to be already simplicial.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 60 , Issue 1 , January 1964 , pp. 39 - 43
Copyright
Copyright © Cambridge Philosophical Society 1964

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References

REFERENCES

(1)Alexander, J. W.A proof of the invariance of certain constants of analysis situs. Trans. American Math. Soc. 16 (1915), 148–154CrossRefGoogle Scholar
(2)Hilton, P. J. and Wylie, A.Homology theory (Cambridge, 1960).CrossRefGoogle Scholar
(3)Lefschetz, S.Topology (American Mathematical Society Colloquium Publication, vol. xii; New York, 1930).Google Scholar
(4)Penrose, R., Whitehead, J. H. C. and Zeeman, E. C.Imbeddings of manifolds in Euclidean space. Ann. of Math. 73 (1961), 613–623CrossRefGoogle Scholar
(5)Whitehead, J. H. C.Simplicial spaces, nuclei and m-groups. Proc. London Math. Soc., 45 (1939), 243–327CrossRefGoogle Scholar