Esnek ve bulanık esnek kümelerin düzgün ve yakınlık uzaylarına uygulanması
Yükleniyor...
Dosyalar
Tarih
2016
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Düzce Üniversitesi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Bu tez çalışmasında, öncelikle esnek küme teorisi kullanılarak esnek düzgün uzaylar tanımlanmış ve bu uzaylar yardımıyla bir esnek topolojik uzay elde edilmiştir. Esnek yakınlık uzaylarıyla ilgili özellikler incelenmiş ve esnek düzgün uzaylar ile ilişkisi araştırılmıştır. Sabit nokta teorisi üzerinde çalışabilmek için esnek elemanlar yardımıyla bir se-düzgün uzay kavramı tanımlanmıştır. Daha sonra bu uzay üzerinde sabit esnek eleman teoremleri elde edilmiştir. Ayrıca bir bulanık esnek komşuluk sistemi kavramı verilmiş ve özellikleri incelenmiştir. Bunun yanı sıra Lowen anlamında bir bulanık esnek düzgün uzay tanımlanarak bulanık esnek topoloji ve bulanık esnek komşuluk sistemi ile ilişkisi araştırılmıştır. Son olarak bulanık esnek yakınlık uzaylarıyla ilgili özellikler incelenerek klasik anlamdaki yakınlık uzaylarıyla ilişkisi elde edilmiştir.
In this thesis, soft uniform spaces first were introduced by using the soft set theory and a soft topological space was obtained with the help of these spaces. The properties about soft proximity spaces were examined and their relation with soft uniform spaces was investigated. In order to study on fixed point theory, the concept of an se-uniform space was defined with the aid of soft elements. Then, fixed soft element theorems were obtained in this space. Also, the concept of a fuzzy soft neighborhood system was given and studied its properties. Moreover, a fuzzy soft uniform space in the sense of Lowen was introduced and investigated its relation with fuzzy soft topology and fuzzy soft neighborhood system. Finally, the properties regarding fuzzy soft proximity spaces were examined and their relation with proximity spaces in classical meaning was established.
In this thesis, soft uniform spaces first were introduced by using the soft set theory and a soft topological space was obtained with the help of these spaces. The properties about soft proximity spaces were examined and their relation with soft uniform spaces was investigated. In order to study on fixed point theory, the concept of an se-uniform space was defined with the aid of soft elements. Then, fixed soft element theorems were obtained in this space. Also, the concept of a fuzzy soft neighborhood system was given and studied its properties. Moreover, a fuzzy soft uniform space in the sense of Lowen was introduced and investigated its relation with fuzzy soft topology and fuzzy soft neighborhood system. Finally, the properties regarding fuzzy soft proximity spaces were examined and their relation with proximity spaces in classical meaning was established.
Açıklama
YÖK Tez No: 430821
Anahtar Kelimeler
Matematik, Mathematics
