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

Year 2008, Volume: 3 Issue: 1, 51 - 59, 01.06.2008

A. Acıkgoz

Abstract

Abstract: An ideal topological space (X,Ï„,I) is said to be an F* – space if A=Cl*(A) for
every open set A ⊂ 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)*⊂ A
for every set A⊂X. It is shown that δI – r – continuity (resp. pre – I – continuity, semi –
δ – 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, δ – I – open set, δ – 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)*⊂ A ise bu taktirde bu uzaya SA*
–uzay denir. SA*-uzayında δI – 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, δ – I – açık küme, δ – I – regüler küme, R – I –
sürekliliğin ayrışımı, ideal topoloji.

Keywords

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

References

• ABD EL – MONSEF ME, LASHIEN EF, NASEF AA, 1992. On I − open sets and I – continuous functions, Kyungpook Mathematical Journal, 32(1), 21–30.
• ACİKGOZ A, NOİRİ T, YUKSEL S, 2004. On δ − I − open sets and decomposition of α − I − continuity, Acta Mathematica Hungarica, 102(4), 349–357.
• ACIKGOZ A, YUKSEL S, 2006. On δ – I – regular sets and two decompositions of R – I – continuity, Far East Journal of Mathematical Sciences, 23, 53–64.
• DONTCHEV J, 1996. On pre – I – open sets and a decomposition of I – continuity, Banyan Mathematical Journal, Vol. 2.
• DONTCHEV J, GANSTER M, ROSE D, 1999. Ideal resolvability, Topology and its Applications, 93, 1–16.
• DONTCHEV J, 1999. Idealization of Ganster – Reilly decomposition theorems, Math. GN/ 9901017, 5 Jan. (Internet).
• DUGUNDJI J, 1966. Topology, Allyn and Bacon, Boston, pp. 92.
• HATIR E, NOIRI T, 2002. On decompositions of continuity via idealization, Acta Mathematica Hungarica , 96, 341–349.
• HATIR E, NOIRI T, 2005. On semi – I – open sets and semi – I – continuous functions, Acta Mathematica Hungarica, 10(4), 345–353.
• HAYASHI E, 1964. Topologies defined by local properties, Mathematische Annalen, 156, 205–215 .
• JANKOVIĆ D, HAMLETT TR, 1990. New topologies from old via ideals, The
• American Mathematical Monthly, 97, 295–310.
• KESKİN A, NOİRİ T, YUKSEL S, 2004. FI – sets and decomposition of RIC – continuity, Acta Mathematica Hungarica, 104(4), 307–313.
• KESKİN A, NOİRİ T, YUKSEL Ş, 2004. Idealization of decomposition theorem,Acta Mathematica Hungarica, 102(4), 269–277.
• KURATOWSKI K, 1966. Topology Vol. 1 (transl.), Academic Press, New York.
• LEVINE N, 1963. Semi – open sets and semi – continuity in topological spaces, The American Mathematical Monthly, 70, 36–41.
• SAMUELS P, 1975. A topology formed from a given topology and ideal, Journal of the London Mathematical Society (2), 10, 409–416.
• YUKSEL S, ACİKGOZ A, NOİRİ T, 2005. On δ − I − continuous functions, Turkish Journal of Mathematics, 29, 39-51.