Esnek Topolojik Uzayların Karşılaştırılması

Öz

Bu çalışmada, esnek topolojik uzayların karşılaştırılması esnek açık küme ve esnek alt küme kavramları yardımı ile incelenmiştir. Esnek topolojik uzay ve esnek açık küme kavramı Shabir ve Naz (2011) tarafından belirli bir evren üzerinde ve sabit bir parametre kümesiyle tanımlanmıştır. İlk olarak bu kavram yardımıyla klasik topolojik uzaylardaki karşılaştırma tanımı dikkate alınarak esnek topolojilerin karşılaştırması yapılmıştır. Daha sonra literatürde Maji ve ark., (2003), Pei ve Miao (2005) ve Çağman ve Enginoğlu (2010) tarafından birbirinden farklı şekilde verilmiş olan esnek alt küme tanımları incelenmiştir ve aralarındaki ilişki belirlenmiştir. Bu ilişki yardımıyla esnek topolojilerin karşılaştırması yapılmıştır. Ayrıca Shabir ve Naz (2011) esnek topolojik uzaylarda iki esnek topolojinin kesişiminin esnek topoloji olduğunu ancak birleşiminin genellikle esnek topoloji olmadığını örnekler ile göstermişlerdir. Ancak bu örnekler problemlidir. Bu makale de bu problemi giderecek örnekler verilmiştir.

Anahtar Kelimeler

• Esnek küme
• Esnek topolojik uzay
• Esnek açık küme
• Esnek alt küme.

Comparisons of Soft Topological Spaces

Öz

In this study, the comparison of soft topological spaces has been examined using the concepts of soft open sets and soft subsets. The concepts of soft topological space and soft open set were defined by Shabir and Naz (2011) over a specific universe and with a fixed set of parameters. First, using this concept, the comparison of soft topologies was performed by considering the comparison definition in classical topological spaces. Subsequently, the definitions of soft subsets given in different ways in the literature by Maji et al. (2003), Pei and Miao (2005), and Çağman and Enginoğlu (2010) were examined, and the relationship between them was determined. The comparison of soft topologies was made using this relationship. Shabir and Naz (2011) demonstrated with examples that the intersection of two soft topologies is a soft topology, but the union is not necessarily a soft topology. However, these examples are problematic. In this article, examples were given to eliminate this problem.

Anahtar Kelimeler

• Soft set
• Soft topological space
• Soft open set
• Soft subset

Kaynakça

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