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İdeal ikili topolojik uzaylarda bazı genelleştirilmiş açık kümeler üzerine

On some generalized open sets in ideal bitopological spaces

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  1. Tez No: 651661
  2. Yazar: IBTISSAM RAJAB BUKHATWA
  3. Danışmanlar: DR. ÖĞR. ÜYESİ SİBEL DEMİRALP
  4. Tez Türü: Doktora
  5. Konular: Matematik, Mathematics
  6. Anahtar Kelimeler: Belirtilmemiş.
  7. Yıl: 2020
  8. Dil: Türkçe
  9. Üniversite: Kastamonu Üniversitesi
  10. Enstitü: Fen Bilimleri Enstitüsü
  11. Ana Bilim Dalı: Matematik Ana Bilim Dalı
  12. Bilim Dalı: Belirtilmemiş.
  13. Sayfa Sayısı: 78

Özet

In this thesis, 〖 γ〗_ij-T-open, γ_ij-semi-T-open,γ_ij-pre-T-open, 〖 γ〗_ij-bT-open and γ_ij-βT-open sets defined fort he first time in the literature and basic properties are given in ideal bitopological spaces with an operation γ:T_ →P(X)by generalizing (i,j)-T-open, (i,j)-semi-T-open,(i,j)-pre-T-open, (i,j)-bT-open, and (i,j)-βT- open sets. This thesis basically consists of four chapters. After the introduction, the necessary basic concepts are given in the second chapter to make the thesis easier to understand. In the third chapter, γ_ij-T-open, γ_ij-semi-T-open,γ_ij-pre-T-open, 〖 γ〗_ij-bT-open and γ_ij-βT-open sets are defined. The relationship between the open sets which are defined is examined. Finally, in the fourth chapter, by the help of generalized open sets 〖(γ,δ)〗_ij-T- continuity, 〖(γ,δ)〗_ij-pre-T- continuity, 〖(γ,δ)〗_ij-𝑏𝔗- continuity, 〖(γ,δ)〗_ij-semi-T- continuity, 〖(γ,δ)〗_ij-βT- continuity are defined and the relations between them are investigated.

Özet (Çeviri)

Generalized open sets play a very important role in general topology and they are now the research topic of many topologists worldwide. Indeed, an important subject in general topology and real analysis concerns the various modified forms of continuity, separation axioms, etc., with the use of generalized open sets. This research area (which is fertile in information) still takes a significant part of the investigations because it has a clear effect on the development of the topological space through the experience of many theories and characteristics of different types of open sets. In this thesis, we introduce and study the concepts of γ_ij-T-open sets ,γ_ij-semi-T-open sets ,γ_ij-pre-T- open sets,γ_ij-b-T-open sets, γ_ij-β-T-open sets by generalizing (i,j)-T- open, (i,j)-preT- open, (i,j)-bT- open,(i,j)-semi-T- open and (i,j)-β-T- open sets, respectively, in ideal bitopological spaces with an operation γ:T_ →P(X).Further, we describe and study (〖γ,δ)〗_ij-Continuous functions in ideal bitoplogical spaces through this generalized open sets, and their related notions. In addition, various examples and counterexamples are given for answers to some questions raised in this study.

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