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θ-compact

Last-modified: 2010-09-01 (水) 22:17:15

Definition 1 Edit

A topological space X is called θ-compact if every cover of the space by θ-open sets has a finite subcover.

Definition 2 Edit

Let X be a topological space and F be its subset. F is called θ-compact if for every cover U of F by open sets of X, there exists a finite members imgtex.fcgi?%5bres=100%5d%7b$V_1%2c%5ccdots%2cV_n$%7d%25.png of U such that imgtex.fcgi?%5bres=100%5d%7b$%5cmathrm%7bint%7d%5cbigcup_%7b1%5cle%20i%5cle%20n%7d%5cmathrm%7bcl%7dV_i$%7d%25.png covers F.

Reference Edit

Definition 1
Mohammad Saleh, Onθ-closed sets and some forms of continuity, Archivum mathematicum (BRNO) Tomus 40 (2004), 383-393.
Definition 2
M. Caldas and G. Navalagi, On weak forms of preopen and preclosed, Archivum Mathematicum (BRNO) Tomus 40 (2004), 119-128.