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Shape morphisms and components of movable compacta


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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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

Item Type:Article
Uncontrolled Keywords:Shape theory; Quotient spaces, decompositions; Ljusternik-Schnirelman (Lyusternik-Shnirelʹman) category of a space
Subjects:Sciences > Mathematics > Geometry
Sciences > Mathematics > Topology
ID Code:17127

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