Top > (Λ,sθ)-closed
HTML convert time to 0.002 sec.


(Λ,sθ)-closed

Last-modified: 2010-11-12 (金) 18:23:21

Definition Edit

Let A be a subset of a topological space X.
By imgtex.fcgi?%5bres=200%5d%7b$%5cLambda_%5ctheta%5e%7b%5cLambda_s%7d%28A%29$%7d%25.png we denote the set imgtex.fcgi?%5bres=100%5d%7b$%5ccap%5c%7b%20B:B%5ctext%7b%20is%20semi-%7d%5ctheta%5ctext%7b-closed%20and%20%7dB%5csubset%20A%20%5c%7d$%7d%25.png (see semi-θ-closed).
A is called imgtex.fcgi?%5bres=100%5d%7b$%5cLambda_%5ctheta%5e%7b%5cLambda_s%7d$%7d%25.png-set if imgtex.fcgi?%5bres=100%5d%7b$%5cLambda_%5ctheta%5e%7b%5cLambda_s%7d%28A%29=A$%7d%25.png.
A is called (Λ,sθ)-closed (or imgtex.fcgi?%5bres=100%5d%7b$%5cLambda_s$%7d%25.png-semi-θ-closed) if A=T∩C for some imgtex.fcgi?%5bres=100%5d%7b$%5cLambda_%5ctheta%5e%7b%5cLambda_s%7d$%7d%25.png-set T and some semi-θ-closed set C.
The complement of a (Λ,sθ)-closed set is called (Λ,sθ)-open (or imgtex.fcgi?%5bres=100%5d%7b$%5cLambda_s$%7d%25.png-semi-θ-open).

Reference Edit

M. Caldas, M. Ganster, D. N. Georgiou, S. Jafari, V. Popa, On a Generalization of Closed Sets, Kyungpook Math. J. 47(2007), 155-164.