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On classes of maps which preserve finitisticness


Koyama, Akira y Morón, Manuel A. (2002) On classes of maps which preserve finitisticness. Proceedings of the American Mathematical Society, 130 (10). pp. 3091-3096. ISSN 0002-9939

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We shall prove the following: ( 1) Let r : X --> Y be a refinable map between paracompact spaces. Then X is finitistic if and only if Y is finitistic. ( 2) Let f : X --> Y be a hereditary shape equivalence between metric spaces. Then if X is finitistic, Y is finitistic.

Tipo de documento:Artículo
Palabras clave:Cell-like maps; cohomological dimension; refinable maps; property-c; spaces; finitistic spaces; refinable maps; c-refinable maps; hereditary shape equivalences; extension dimension; cohomological dimension
Materias:Ciencias > Matemáticas > Topología
Código ID:15291

F. Ancel, Proper hereditary shape equivalence property C, Topology and its Appl., 19(1985), 71-74. MR 86g:54026

G. E. Bredon, Introduction to compact transformation groups, Academic Press, 1972, New York. MR 54:1265

A. Chigogidze and V. Valov, Extension dimension and refinable maps, preprint(1999).

S. Deo and A. R. Pears, A completely finitistic space is finite-dimensional, Bull. London Math. Soc., 17(1985), 49-51. MR 85k:54041

S. Deo and T. B. Singh, On the converse of some theorems about orbit spaces, J. London Math. Soc., 25(1982), 162-170. MR 83k:54039

On certain constructions in finitistic spaces, Internat. J. Math. Math. Sci., 6(1983), 477-482. MR 85c:54058

S. Deo, T. B. Singh, and R. A. Shukra, On an extension of localization theorem and generalized Conner conjecture, Trans. Amer. Math. Soc., 269(1982), 395-402. MR 83a:57051

S. Deo and H. S. Tripathi, Compact Lie group actions on finitistic spaces, Topology, 21(1982), 393-399. MR 83k:54042

J. J. Dijkstra, A dimension raising hereditary shape equivalence, Fund. Math., 149(1996), 265-274. MR 97f:54040

J. J. Dijkstra and J. Mogilski, Countable dimensionality and dimension raising cell-like maps, 80(1997), 73-79. MR 98i:54017

A. N. Dranishnikov, Cohomological dimension is not preserved under Stone-Cech compactification, Comptes Rendus Bulgarian Acad. of Sci., 41(1988), 9-10. MR 90e:55002

J. Dydak, S. N. Mishra and R. A. Shukla, On finitistic spaces, Topology and its Appl., 97(1999), 217-229. MR 2000i:55003

J. Dydak and J. Walsh, Spaces without cohomological dimension preserving compactifications, Proc. Amer. Math. Soc., 113(1991), 1155-1162. MR 92c:54039

Jo Ford and J. Rogers, Jr., Refinable maps, Colloq. Math., 39(1978), 263-269. MR 80d:54009

D. Garity and D. Rohm, Property C, refinable maps and dimension raising maps, Proc.Amer. Math. Soc., 98(1986), 336-340. MR 87i:54077

Y. Hattori, A note on finitistic spaces, Questions and Answers Gen. Topology, 3(1985), 47-55. MR 86m:54025

Finitistic spaces and dimension, Houston J. Math., 25(1999), 687-696.

H. Kato, A note on infinite dimension under refinable maps, Proc. Amer. Math. Soc.,88(1983), 177-180. MR 84c:54064

H. Kato and A. Koyama, A role of refinable maps - a survey, Topology Proc., 11(1986), 317-348. MR 89f:54030

A. Koyama, Refinable maps in dimension theory, Topology and its Appl., 17(1984), 247-255. MR 86d:54056

Refinable maps in dimension theory II, Bull. Pol. Math. Soc., 42(1994), 255-261. CMP 2001:07

A. Koyama and R. Sher, Approximable dimension and acyclic dimension, Fund. Math., 152(1997), 43-53.

V. I. Kuz'minov, Homological dimension theory, Russian Math. Surveys, 23(1968), 1-45. MR 39:2158

M. Levin, Some examples in cohomological dimension theory, preprint(1999).

R. Millspaugh, Proper hereditary shape equivalences preserve small weak infinite dimensionality, Proc. Amer. Math. Soc., 90(1984), 1055-1061. MR 91d:54041

L. Rubin and P. Schapiro, Cell-like maps onto non-compact spaces of finite cohomological dimension, Topology and its Appl., 27(1987), 221-244. MR 89b:55002

Compactifications which preserve cohomological dimension, Glasnik Mat., 28(48)(1993), 155-165. MR 95g:54029

R. G. Swan, A new method in fixed point theory, Comment. Math. Helv., 34(1960), 1-16. MR 22:5978

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