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semi-θ-closed

Last-modified: 2010-11-12 (金) 18:26:01

Definition Edit

Let A be a subset of a topological space X.
The intersection of all semiclosed sets containing A is called semi-closure of A (denoted by sCl(A)).
By imgtex.fcgi?%5bres=100%5d%7b$sCl_%5ctheta%20%28A%29$%7d%25.png we denote the set of all x in X such that imgtex.fcgi?%5bres=100%5d%7b$sCl%28O%29%5ccap%20A%5cne%20%5cemptyset$%7d%25.png for every semiopen set O of X containing x (called semi-θ-closure of A).
A is called semi-θ-closed if imgtex.fcgi?%5bres=100%5d%7b$sCl_%5ctheta%20%28A%29=A$%7d%25.png.
The complement of a semi-θ-closed is called 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.