Publication: Prabir Roy's space Δ as a counterexample in shape theory
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1986-09
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American Mathematical Society
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Abstract
In this note we use the space Δ in order to prove that a result concerning movability and mutational retractions cannot be transferred from the compact to the arbitrary metrizable case
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K. Borsuk, Theory of shape, Monogr. Mat. 59, PWN, Warsaw, 1975.
R. Engelking, General topology, Monogr. Mat. 60, PWN, Warsaw, 1977.
R. H. Fox, On shape, Fund. Math. 74 (1972), 47-71.
S. Godlewski, Mutational retracts and extensions of mutations, Fund. Math. 84 (1974), 47-65.
P. Nyikos, Prabir Roy's space Δ is not N-compact, General Toplogy Appl. 3 (1973), 197-210.
P. Roy, Nonequality of dimensions for metric spaces, Trans. Amer. Math. Soc. 134 (1968), 117-132.
K. Sakai, Some properties of MAR and MANR, Tôhoku Math. J. 30 (1978), 351-366.
S. Spiez, A majorant for the family of all movable shapes, Bull. Acad. Polon. Sci. 21 (1973), 615-620.