Rodríguez Sanjurjo, José Manuel (1988) Shape morphisms and components of movable compacta. Mathematical Proceedings of the Cambridge Philosophical Society, 103 (Part 3). pp. 481-486. ISSN 0305-0041
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Official URL: http://journals.cambridge.org/abstract_S0305004100065087
The author treats shape properties which movable compacta and their nonmovable components inherit from their movable components. First he shows that shape morphisms of movable compacta are completely determined by their restrictions to movable components. Then he gives a necessary and sufficient condition for a shape morphism α between movable compacta X and Y to be an isomorphism. Such a condition is given in terms of the morphisms induced by α between the components of X and Y . This result improves a result of Dydak and Segal in the case of movable compacta. Finally, he shows that the shape category of a movable compactum is completely determined by the shape category of its movable components. The shape category is a numerical shape invariant introduced by Borsuk which in the case of polyhedra agrees with the Lyusternik-Shnirelʹman category
|Uncontrolled Keywords:||Shape theory; Quotient spaces, decompositions; Ljusternik-Schnirelman (Lyusternik-Shnirelʹman) category of a space|
|Subjects:||Sciences > Mathematics > Geometry|
Sciences > Mathematics > Topology
 M. ALONSO-MORON. Prabir Roy's space A as a counter-example in shape theory. Proc. Artier. Math. Soc. 98 (1986), 187-188.
M. ALONSO-MORON. On the problem of components in Shape Theory for metrizable spaces. Preprint.
B. J. BALL. Partitioning shape-equivalent spaces. Bull. Acad. Polon. Sci. Ser. Sci. Math. 29 (1981), 491-497.
K. BORSUK. Theory of Retracts. Monografie Matematyczne no. 44 (Polish Scientific Publishers, 1967).
K. BORSUK. On movable compacta. Fund. Math. 66 (1969/70), 137-146.
K. BOESUK. Theory of Shape. Monografie Matematyczne no. 59 (Polish Scientific Publishers, 1975).
K. BORSUK. On the Lusternik-Schnirelman category in the theory of shape. Fund. Math. 99 (1978), 35-42.
Z. CERIN. Locally compact spaces ^"-tame at infinity. Publ. Inst. Math. (Beograd) (N.S.) 22 (36) (1977), 49-59.
J. DYDAK and J. SEGAL. Shape Theory: An Introduction. Lecture Notes in Math. vol. 688 (Springer-Verlag, 1978).
S. GODLEWSKI. On the shape of MAR and MANR-spaces. Fund. Math. 88 (1975), 87-94.
S. T. Hu. Theory of Retracts (Wayne State University Press, 1965).
Y. KODAMA. Decomposition spaces and shape in the sense of Fox. Fund. Math. 97 (1977), 199-208.
S. MARDESIC and J. SEGAL. Shape Theory (North-Holland, 1982).
S. NOWAK. Remarks on same shape properties of the components of movable compacta. Bull. Acad. Polon. Sci. Se'r. Sci. Math. 27 (1979), 315-319.
J. OLEDZKI. On the space of components of an R-movable compactum. Bull. Acad. Polon. Sci. Se'r. Sci. Math. 22 (1974), 1239-1244.
P. ROY. Failure of equivalence of dimension concepts for metric spaces. Bull. Amer. Math. Soc. 68 (1962), 609-613.
J. M. R. SANJURJO. On a theorem of B. J. Ball. Bull. Acad. Polon. Sci. Se'r. Sci. Math. 33 (1985), 177-180.
J. M. R. SANJURJO. On the shape category of compacta. J. London Math. Soc. (2) 34 (1986), 559-567.
J. SEGAL and S. SPIEZ. A non-movable space with movable components. Preprint.
|Deposited On:||16 Nov 2012 10:01|
|Last Modified:||07 Feb 2014 09:42|
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