*Definition [#ae202e75]
Let A be a subset of a topological space X.
By &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=200%5d%7b$%5cLambda_%5ctheta%5e%7b%5cLambda_s%7d%28A%29$%7d%25.png); we denote the set &ref(http://www.eaflux.com/imgtex/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 &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$%5cLambda_%5ctheta%5e%7b%5cLambda_s%7d$%7d%25.png);-set if &ref(http://www.eaflux.com/imgtex/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 &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$%5cLambda_s$%7d%25.png);-semi-θ-closed) if A=T∩C for some &ref(http://www.eaflux.com/imgtex/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 &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$%5cLambda_s$%7d%25.png);-semi-θ-open).
*Reference [#a7cff836]
M. Caldas, M. Ganster, D. N. Georgiou, S. Jafari, V. Popa, ''On a Generalization of Closed Sets'', Kyungpook Math. J. 47(2007), 155-164.