Lupianez, Francisco Gallego
(1987)
*Alpha-paracompact subsets and well-situated subsets.*
Questions and answers in general topology , 5
.
pp. 293-302.
ISSN 0918-4732

## Abstract

We study -paracompact subsets, defined by C. E. Aull. Here we obtain some covering properties of -paracompact subsets which are similar to properties of paracompact spaces. In particular, we characterize -paracompact subsets in regular spaces. Moreover we study the behaviour of -paracompact subsets under perfect mappings.

Then we consider R. Telg´arsky’s well-situated subsets. The properties of -paracompact subsets yield properties of well-situated subsets. Well-situated subsets are related to

Tamano’s problem (i.e.: to give an intrinsic description of those T2 spaces X such that X × Y is paracompact for each paracompact T2 space Y) which remains open.

Finally, we solve a problem of Telg´arsky establishing that: In the realm of T2 spaces,the class is perfect.

Item Type: | Article |
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Uncontrolled Keywords: | -paracompact subsets; Perfect mappings; Well-situated subsets; Class |

Subjects: | Sciences > Mathematics > Topology |

ID Code: | 15340 |

Deposited On: | 24 May 2012 09:28 |

Last Modified: | 28 Oct 2013 18:20 |

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