Compact factors in finally compact products of topological spaces |
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Authors: | Paolo Lipparini |
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Institution: | Dipartimento di Matematica, Viale della Ricerca Scientifica, II Università di Roma (Tor Vergata), I-00133 Rome, Italy |
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Abstract: | We present instances of the following phenomenon: if a product of topological spaces satisfies some given compactness property then the factors satisfy a stronger compactness property, except possibly for a small number of factors.The first known result of this kind, a consequence of a theorem by A.H. Stone, asserts that if a product is regular and Lindelöf then all but at most countably many factors are compact. We generalize this result to various forms of final compactness, and extend it to two-cardinal compactness. In addition, our results need no separation axiom. |
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Keywords: | primary 54B10 54D20 secondary 03E05 |
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