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 Lindelof 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.
Lipparini, P. (2006). Compact factors in finally compact products of topological spaces. TOPOLOGY AND ITS APPLICATIONS, 153(9), 1365-1382 [10.1016/j.topol.2005.04.002].
Compact factors in finally compact products of topological spaces
LIPPARINI, PAOLO
2006-01-01
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 Lindelof 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.