continuous functions induced by shape morphisms1 - American ...
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PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 41, Number I, November 1973
CONTINUOUS FUNCTIONS INDUCED BY SHAPE MORPHISMS1 JAMES KEESLING Abstract. Let C denote the category of compact Hausdorff spaces and continuous maps and H:C-*HC the homotopy functor to the homotopy category. Let S : C--A are continuous with f(x)=g(x)=0, then S(f) = S(g) implies
H(f)^Hig). The key to the proofs of these theorems is Theorem 68 of [8, p. 326] which we state before beginning the proofs of the above theorems. License or copyright restrictions may apply to redistribution; see http://www.ams.org/journal-terms-of-use
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CONTINUOUS FUNCTIONS INDUCED BY SHAPE MORPHISMS
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1.3. Definition. Let @={GX; nxß; a.-—ß~Ax+y be defined by Jx+1(x, ?) = (/'(*, t), J"ix, t)) e A' x ker q—Aa+1. Then in this case also {Jx:a^ß} has properties (1), (2), and (3) above. Proceeding by transfinite induction we get a collection of maps {Jx:a.co0 and assume that for all cox
