A DECOMPOSITION OF CONTINUITY ON F– SPACES AND MAPPINGS ON SA– SPACES

Abstract: An ideal topological space (X,Ï„,I) is said to be an F* – space if A=Cl*(A) for every open set A âŠ‚ X. In this paper, a decomposition of continuity on F* – spaces is introduced. An ideal topological space (X,Ï„,I) is said to be an SA* – space if (A)*âŠ‚ A for every set AâŠ‚X. It is shown that Î´I – r – continuity (resp. pre – I – continuity, semi – Î´ – I – continuity, * – perfect continuity) is equivalent to R – I – continuity (resp. R – I – continuity, t – I – continuity, * – dense – in – itself continuity) if the domain is an SA* – space. Key words: R – I – open set, Î´ – I – open set, Î´ – I – regüler set, decomposition of R – I – continuity, topological ideal. Mathematics Subject Classification (2000): Primary 54C08, 54A20; Secondary 54A05, 54C10. F*-UZAYLARDA SÜREKLİLİĞİN BİR AYRIŞIMI VE SA* -UZAYLARDA DÖNÜŞÜMLER Özet: Eğer (X, Ï„, I) uzayının her açık A alt kümesi için A = Cl*(A) ise bu taktirde bu uzaya F* – uzay denir. Bu çalışmada, F* – uzayında sürekliliğin bir ayrışımı verildi. Eğer (X, Ï„, I) uzayının her açık A alt kümesi için (A)*âŠ‚ A ise bu taktirde bu uzaya SA* –uzay denir. SA*-uzayında Î´I – r –süreklilik (sırasıyla, pre-I-süreklilik, semi-Isüreklilik, * – perfect süreklilik) ile R – I – sürekliliğin (sırasıyla, R – I – süreklilik, t – I – süreklilik, kendi içinde *-yoğun süreklilik) birbirine eşdeğer olduğu gösterildi. Anahtar Kelimeler: R-I-açık küme, Î´ – I – açık küme, Î´ – I – regüler küme, R – I – sürekliliğin ayrışımı, ideal topoloji.

Anahtar Kelimeler:

R-I-açık küme, δ – I – açık küme, δ – I – regüler küme, R – I – sürekliliğin ayrışımı, ideal topoloji

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