A note on absolute approximate retracts

• Autorzy: Martin J.
• Języki publikacji: EN

Abstrakty

EN

The notion of an absolute approximate retract for a class Q of topological spaces (or an AAR(Q)-space) generalizes the concept of an absolute retract for the class Q. For many classes Q, it is shown that AAR(Q)-spaces are preserved under retraction mappings and that a fully normal AAR(Q)-space X must be contractible and can be expressed as a product of finite-dimensional compacta if and only if X is homeomorphic to a cube or is a finite-dimensional AR-space.

Słowa kluczowe

EN

absolute (neighbourood) retract; adjunction space; retract

PL

przestrzeń doklejona; retrakt; retrakt absolutny otoczeniowy

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2001
• Tom: Vol. 49, no 4
• Strony: 355--359
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Martin J.

• Department of Mathematics and Statistics, University of Saskatchewan, 106,,Viggins Road, Saskatoon, SK S7N 5E6 Canada

Bibliografia

• [1] K. Borsuk, Theory of retracts, PWN, Warszawa 1967.
• [2] T. A. Chapman, Lectures on Hilbert cube manifolds,CBMS Regional Conf. Ser. in Math., no. 28, Amer. Math. Soc., Providence, R.I. 1976.
• [3] 0. Hanner, Retraction and extension of metric and non-metric spaces, Ark. Mat., 2 (1952) 315-360.
• [4] S. T. Hu, Theory of retracts, Wayne State University Press, Detroit 1965.
• [5] J. R. Martin, A generalization of absolute retracts, Proc. Amer. Math. Soc., 52 (1975) 409-413.
• [6] J. R. Martin, An example of a contractible LC∞compactum which is not an absolute approximate retract, Bull. Pol. Ac.: Math., 25 (1977) 489-492.
• [7] J. R. Martin, Absolute approximate retracts and AR-spaces, Canad. J. Math., 33 (1981) 279-301.
• [8] J. R. Martin, Neighborhood contractible spaces, Proc. Amer. Math. Soc., 87 (1983) 154-158.
• [9] J. R. Martin, Factors of compact absolute fixed point sets, Houston J. Math., to be published.