Hostname: page-component-745bb68f8f-mzp66 Total loading time: 0 Render date: 2025-01-18T20:56:13.764Z Has data issue: false hasContentIssue false
  • English
  • Français

A characterisation of the absolute quasi-retracts in a class of acyclic continua

Published online by Cambridge University Press:  17 April 2009

V.N. Akis  and
D.W. Curtis
V.N. Akis
Affiliation:
California State University, Los Angeles, California 90032
D.W. Curtis
Affiliation:
Louisiana State University, Baton Rouge, Louisiana 70803
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The class of quasi-retracts of AR's (AQR's) was first considered by Stallings, who observed that every AQR has the fixed point property. More recently, it has been shown that the class of AQR's is closed with respect to the operations of taking cones, suspensions, or products with AR's, and that no AQR separates a Euclidean space. In this paper we show that every AQR is acyclic, and we obtain a simple, direct characterization of the AQR's in a certain class of acyclic continua.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 36 , Issue 2 , October 1987 , pp. 227 - 237
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Akis, V.N., “Fixed point theorems and almost continuity”, Fund. Math. 121 (1984), 133–142.CrossRefGoogle Scholar
[2]Akis, V.N., “Almost continuous extensions”, submitted to Houston J. Math.Google Scholar
[3]Bell, H., “On fixed point properties of plane continua”, Trans. Amer. Math. Soc. 128 (1967), 539–548.CrossRefGoogle Scholar
[4]Chapman, T.A., “On some applications of infinite-dimensional manifolds to the theory of shape”, Fund. Math. 76 (1972), 181–193.CrossRefGoogle Scholar
[5]Dugundji, J., “Locally equiconnected spaces and absolute neighbourhood retracts”, Fund. Math. 57 (1965), 187–193.CrossRefGoogle Scholar
[6]Hu, S.T., Theory of retracts (Wayne State Univ. Press, Detroit, 1965).Google Scholar
[7]Knill, R.J., “Cones, products and fixed points”, Fund. Math. 60 (1967), 35–46.CrossRefGoogle Scholar
[8]Rosen, H., “Non-separating almost continuous retracts of In”, Proc. Amer. Math. Soc. 91 (1984), 118–122.Google Scholar
[9]Sieklucki, K., “On a class of plane acyclic continua with the fixed point property”, Fund. Math. 63 (1968), 257–278.CrossRefGoogle Scholar
[10]Stallings, J., “Fixed point theorems for connectivity maps”, Fund. Math. 47 (1959), 249–263.CrossRefGoogle Scholar