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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).

Record Type:	Electronic resources : Monograph/item
Title/Author:	Tukey quotients, pre-ideals, and neighborhood filters with calibre (omega 1, omega)./
Author:	Morgan, Jeremiah.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2016,
Description:	162 p.
Notes:	Source: Dissertation Abstracts International, Volume: 78-05(E), Section: B.
Contained By:	Dissertation Abstracts International78-05B(E).
Subject:	Mathematics. -
Online resource:	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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100 1 $a Morgan, Jeremiah. $3 3343195
245 1 0 $a Tukey quotients, pre-ideals, and neighborhood filters with calibre (omega 1, omega).
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2016
300 $a 162 p.
500 $a Source: Dissertation Abstracts International, Volume: 78-05(E), Section: B.
500 $a Adviser: Paul Gartside.
502 $a Thesis (Ph.D.)--University of Pittsburgh, 2016.
520 $a 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.
590 $a School code: 0178.
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
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710 2 $a University of Pittsburgh. $3 958527
773 0 $t Dissertation Abstracts International $g 78-05B(E).
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856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10298821