Federer-Čech Couples
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In (5),I considered two-term conditions in π-exact couples, of which the exact couple of Federer (7) is an example. Let M(X, Y)be the space of all maps from X to Y with the compact-open topology. Our aim in this paper is to construct a π-exact couple , where Xis a finite-dimensional (in the sense of Lebesgue) metric space and , a certain (rather large) class of spaces. Specifically, is the class of all topological spaces Xwhich possess the following property (P).(P) Let Y be a (possibly infinite) simplicial complex. There exists x0 ∈ X and y0 ∊ Y such that [X, x0]≃ [Y, y0].In § 5 it will be seen that contains all CW complexes and all metric absolute neighbourhood retracts (ANR)s.
1993 ◽
Vol 16
(2)
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pp. 259-266
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1977 ◽
Vol 23
(1)
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pp. 46-58
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2001 ◽
pp. 322-336
2017 ◽
Vol 20
(K2)
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pp. 107-116
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1985 ◽
Vol 38
(1)
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pp. 118-129
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1995 ◽
Vol 125
(4)
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pp. 739-758