Publication:
Quasicomponents and shape theory

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1988
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Auburn University
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The authors give a definition of a function ˇ : SH! TOP, which in a sense is an anlogue of the Borsuk functor , where (X) is the space of the components of X, with the change from components to quasi-components. Several properties of this functor are proved.
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K. Borsuk, Theory of shape, Polish Scientific Publishers, Warsaw 1975. B. J. Ball, Shapes of saturated subsets of compacta, Colloq. Math. 24 (1974), 241-246. B. J. Ball, Quasicompactifications and shape theory, Pacific J. Math. 84 (1979), 251-259. B. J. Ball, Partitioning shape-equivalent spaces, Bull. Acad. Pol. Sci. 29 (1981), 491-497. J. Dydak and G. Kozlowski, A generalization of the Vietoris-Begle theorem, Proc. Amer. Math. Soc. 102 (1988), 209-212. J. Dydak and J. Segal, Shape theory: An introduction, Lecture Notes in Math. 688, Springer Verlag, 1978, 1-150. J. Dydak, J. Segal and Stanislaw Spiez, A nonmovable space with movable components, Proceedings of The Amer. Math. Soc. (to appear) R. Engelking, Outline of general topology, NorthHolland Publishing Co., Amsterdam 1968. S. Godlewski, On components of MANR-spaces, Fund. Math. 114 (1981), 87-94. S. T. Hu, Theory of retracts, Wayne State University Press, Detroit, 1965. M. A. Morón, Upper semicontinuous decompositions and movability in metric spaces, Bull. Acad. Pol. Sci. 35 (1987), 351-357. S. Nowak, Some properties of fundamental dimension, Fund. Math. 85 (1974), 211-227. J. M. R. Sanjurjo, On a theorem of B. J. Bal, Bull. Acad. Pol. Sci. 33 (1985), 177-180.
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