Retractive product spaces. (English) Zbl 0707.54006
Summary: A completely regular Hausdorff space X is called retractive if there is a retraction from \(\beta\) X onto \(\beta\) \(X\setminus X\). A product space is retractive if and only if all factors are compact but one which is retractive.
MSC:
| 54B10 | Product spaces in general topology |
| 54C15 | Retraction |
| 54D35 | Extensions of spaces (compactifications, supercompactifications, completions, etc.) |
References:
| [1] | Comfort, W. W., Retractions and other continuous maps from βX onto BX (X\), Trans. Amer. Math. Soc., 114, 1-9 (1965) · Zbl 0132.18104 |
| [2] | Conway, J. B., Projections and retractions, Proc. Amer. Math. Soc., 17, 843-847 (1966) · Zbl 0151.29902 |
| [3] | Glicksberg, I., Stone-Čech compactifications of products, Trans. Amer. Math. Soc., 90, 369-382 (1959) · Zbl 0089.38702 |
| [4] | van Douwen, E. K., Retractions from βX onto βX (X\), Gen. Topology Appl., 9, 169-173 (1978) · Zbl 0386.54008 |
| [5] | Walker, R. C., The Stone-Čech Compactification (1974), Springer: Springer Berlin · Zbl 0292.54001 |
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