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

ProQuest Information and Learning Co.

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

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Tukey quotients, pre-ideals, and neighborhood filters with calibre (omega 1, omega)./
Author:	Morgan, Jeremiah.
Description:	1 online resource (162 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 78-05(E), Section: B.
Contained By:	Dissertation Abstracts International78-05B(E).
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
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). - 1 online resource (162 pages)

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

Thesis (Ph.D.)

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

Mode of access: World Wide Web

ISBN: 9781369418361Subjects--Topical Terms:

527692
Mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Tukey quotients, pre-ideals, and neighborhood filters with calibre (omega 1, omega).
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020 $a 9781369418361
035 $a (MiAaPQ)AAI10298821
035 $a AAI10298821
040 $a MiAaPQ $b eng $c MiAaPQ
099 $a TUL $f hyy $c available through World Wide Web
100 1 $a Morgan, Jeremiah. $3 1180787
245 1 0 $a Tukey quotients, pre-ideals, and neighborhood filters with calibre (omega 1, omega).
264 0 $c 2016
300 $a 1 online resource (162 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertation Abstracts International, Volume: 78-05(E), Section: B.
500 $a Adviser: Paul Gartside.
502 $a Thesis (Ph.D.) $c University of Pittsburgh $d 2016.
504 $a Includes bibliographical references
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.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 527692
650 4 $a Theoretical mathematics. $3 1180455
655 7 $a Electronic books. $2 local $3 554714
690 $a 0405
690 $a 0642
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a University of Pittsburgh. $3 1178873
773 0 $t Dissertation Abstracts International $g 78-05B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10298821 $z click for full text (PQDT)

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