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On the shape category of compacta



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Rodríguez Sanjurjo, José Manuel (1986) On the shape category of compacta. Journal of the London Mathematical Society. Second Series, 34 (Part 3). pp. 559-567. ISSN 0024-6107

URL Oficial: http://jlms.oxfordjournals.org/content/s2-34/3/559.short

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K. Borsuk [Fund. Math. 99 (1978), no. 1, 35–42] extended the classical notion of Lyusternik-Shnirelman category (briefly L-S category) to the theory of shape and thereby introduced a shape invariant coefficient for a compactum X . This was subsequently generalized for all topological spaces by V. V. Agaronyan and Yu. M. Smirnov [Soviet Math. Dokl. 20 (1979), no. 3, 516–518] and Z. Čerin [Houston J. Math. 5 (1979), no. 2, 169–182]. The author studies the shape L-S category of compacta and proves, among other things, that the coefficients of two compacta are equal provided there exists a refinable map between them. A new shape invariant called "the coefficient of movability'' is given and some of its properties for shape fibrations are studied. Some properties of Borsuk's coefficient λ(X) introduced in his aforementioned paper are given. Several relations, equalities and inequalities, between these coefficients are also given.

Tipo de documento:Artículo
Palabras clave:Shape theory
Materias:Ciencias > Matemáticas > Geometría
Ciencias > Matemáticas > Topología
Código ID:17124
Depositado:16 Nov 2012 09:23
Última Modificación:16 Nov 2012 09:23

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