Doku uzaylarının kompaktlaştırmaları
Compactifications of texture spaces
- Tez No: 216418
- Danışmanlar: DOÇ.DR. MURAT DİKER
- Tez Türü: Doktora
- Konular: Matematik, Mathematics
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 2007
- Dil: Türkçe
- Üniversite: Hacettepe Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Matematik Ana Bilim Dalı
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 112
Özet
Özet yok.
Özet (Çeviri)
The aim of this thesis is to form a compactification theory for ditopological texture spaces and is to present an approach for the well?known compactifications as Wallman and Stone?C´ech compactifications in General Topology. The first chapter is devoted to an overview on the subject. For the sake of completeness, the second chapter contains the well?known basic concepts and results which are related to the lattice theory, textures, direlations, difunctions. In the third chapter, the restrictions of direlations and difunctions for principal subtextures are discussed and the inclusion difunction is defined. Further, some basic results on restrictions are given. In the fourth chapter, the concept of difilters defined and some basic properties of maximal difilters are presented. Then, aWallman type compactification of weakly T0 and s?bi R0 ditopological texture spaces is constructed in terms of difunctions. In the last part of this chapter, defining the dicovering finite binormality of ditopological texture spaces, a characterization of Wallman compactifications of textures is given and some examples are presented. Hutton spaces play an important role in the theory of fuzzy topological spaces and therefore, the fifth chapter is devoted to the constructions of Wallman compactifications of Hutton spaces. In the sixth chapter, set separating difunctions are defined and a characterization of complete biregularity of ditopological texture spaces is given using set separating difunctions. Moreover, the evaluation difunction is defined and then an approach is given for the Stone?C´ech type compactifications of texture spaces. Finally, it is proved that the Stone?C´ech compactification of a completely regular topological space can be obtained using the highly economic structure of the unit texture. It is also proved that if the product of any family of ditopological plain texture spaces is completely biregular then every space in this family is also completely biregular. Further, under a certain condition, it is shown that the Stone?C´ech compactifications of plain texture spaces can be obtained.
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