Tukey quotients, pre-ideals, and neighborhood filters with calibre (omega 1, omega)
出版項
2016
說明
1 online resource (162 pages)
文字
text
無媒介
computer
成冊
online resource
附註
Source: Dissertation Abstracts International, Volume: 78-05(E), Section: B
Adviser: Paul Gartside
Thesis (Ph.D.) University of Pittsburgh 2016
Includes bibliographical references
This work seeks to extract topological information from the order-properties of certain preideals and pre-filters associated with topological spaces. In particular, we investigate the neighborhood filter of a subset of a space, the pre-ideal of all compact subsets of a space, and the ideal of all locally finite subcollections of an open cover of a space. The class of directed sets with calibre (o1; o) (i.e. those whose uncountable subsets each contain an infinite subset with an upper bound) play a crucial role throughout our results. For example, we prove two optimal generalizations of Schneider's classic theorem that a compact space with a G delta diagonal is metrizable. The first of these can be stated as: if X is (countably) compact and the neighborhood filter of the diagonal in X2 has calibre (o 1; o) with respect to reverse set inclusion, then X is metrizable. Tukey quotients are used extensively and provide a unifying language for expressing many of the concepts studied here
Electronic reproduction. Ann Arbor, Mich. : ProQuest, 2018
