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Tukey quotients, pre-ideals, and nei...

Morgan, Jeremiah.

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Tukey quotients, pre-ideals, and neighborhood filters with calibre (omega 1, omega).

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Tukey quotients, pre-ideals, and neighborhood filters with calibre (omega 1, omega)./
作者:	Morgan, Jeremiah.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2016,
面頁冊數:	162 p.
附註:	Source: Dissertation Abstracts International, Volume: 78-05(E), Section: B.
Contained By:	Dissertation Abstracts International78-05B(E).
標題:	Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10298821
ISBN:	9781369418361

Tukey quotients, pre-ideals, and neighborhood filters with calibre (omega 1, omega).
Morgan, Jeremiah.

Tukey quotients, pre-ideals, and neighborhood filters with calibre (omega 1, omega). - Ann Arbor : ProQuest Dissertations & Theses, 2016 - 162 p.

Source: Dissertation Abstracts International, Volume: 78-05(E), Section: B.

Thesis (Ph.D.)--University of Pittsburgh, 2016.

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.

ISBN: 9781369418361Subjects--Topical Terms:

515831
Mathematics.

Tukey quotients, pre-ideals, and neighborhood filters with calibre (omega 1, omega).
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