Complutense University Library

On classes of maps which preserve finitisticness


Koyama, Akira and 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

[img] PDF
Restringido a Repository staff only hasta 31 December 2020.


Official URL:


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.

Item Type:Article
Uncontrolled Keywords:Cell-like maps; cohomological dimension; refinable maps; property-c; spaces; finitistic spaces; refinable maps; c-refinable maps; hereditary shape equivalences; extension dimension; cohomological dimension
Subjects:Sciences > Mathematics > Topology
ID Code: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

Deposited On:21 May 2012 09:41
Last Modified:06 Feb 2014 10:21

Repository Staff Only: item control page