Biblioteca de la Universidad Complutense de Madrid

Finite approximations to Cech homology

Impacto

Giraldo, A. y Morón, Manuel A. y Romero Ruiz del Portal, Francisco y Rodríguez Sanjurjo, José Manuel (2001) Finite approximations to Cech homology. Journal of Pure and Applied Algebra, 163 (1). pp. 81-92. ISSN 0022-4049

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URL Oficial: http://www.sciencedirect.com/science/article/pii/S0022404900001584




Resumen

We show in this paper how to represent intrinsically Cech homology of compacta, in terms of inverse limits of discrete approximations. We establish some relations between inverse limits and non-continuous homotopies and, as a consequence, we get a strong form of the classical continuity property of Cech homology.


Tipo de documento:Artículo
Palabras clave:Shape; homology theory
Materias:Ciencias > Matemáticas > Topología
Código ID:15374
Referencias:

K. Borsuk, Theory of Retracts, Monografie Matematyczne, vol. 44, Polish Scientific Publishers, Warszawa, 1967.

E. Cech, The Mathematical Legacy of Eduard Cech, M. Katetov, P. Simon (Eds.), BirkhaTuser, Basel, 1993.

Z. Cerin, Proximate topology and shape theory, Proc. Royal Soc. Edinburgh 125 (1995) 595– 615.

J. Dydak, J. Segal, Shape Theory: An Introduction, Lecture Notes in Math., vol. 688, Springer, Berlin, 1978.

S. Eilenberg, N. Steenrod, Foundations of Algebraic Topology, Princeton University Press, Princeton, 1952.

J.E. Felt, ε-continuity and shape, Proc. Amer. Math. Soc. 46 (1974) 426 – 430.

M.J. Greenberg, Lectures on Algebraic Topology, W.A. Benjamin, New York, 1967.

C. Ho, On a stability theorem for the fixed point property, Fund. Math. 111 (1981) 169–177.

R. Kieboom, An intrinsic characterization of the shape of paracompacta by means of non-continuous single-valued maps, Bull. Belg. Math. Soc. 1 (1994) 701–711.

V.L. Klee, Stability of the fixed point property, Colloq. Math. 8 (1961) 43– 46.

V.L. Klee, A. Yandl, Some proximate concepts in topology, in: Symposia Math. Publ. Inst. Naz. Di Alta Matematica, vol. 16, Academic Press, New York, 1974, pp. 21–39.

K. Mischaikov, M. Mrozek, Chaos in the Lorentz equations: a computer assisted proof, Bull. Amer. Math. Soc. 32 (1995) 66 –72.

J.M.R. Sanjurjo, A non-continuous description of the shape category of compacta, Quart. J. Math. Oxford 40 (2) (1989) 351–359.

J.M.R. Sanjurjo, Stability of the fixed point property and universal maps, Proc. Amer. Math. Soc. 105 (1989) 221–230.

A. Szymczak, A combinatorial procedure for finding isolating neighbourhoods and index pairs, Proc. Royal Soc. Edinburgh A 127 (1997) 1075 –1088.

Depositado:25 May 2012 08:37
Última Modificación:06 Feb 2014 10:23

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