On Semicompact Sets and Associated Properties - Mohammad S. Sarsak (International Journal of Mathematics and Mathematical Sciences)
We continue the study of semicompact sets in a topological space. Several properties, mapping properties of semicompact sets are studied. A special interest to 𝑆𝐶𝑆 spaces is given, where a space 𝑋 is 𝑆𝐶𝑆 if every subset of 𝑋 which is semicompact in 𝑋 is semiclosed; we study several properties of such spaces, it is mainly shown that a semi-𝑇2 semicompact space is 𝑆𝐶𝑆 if and only if it is extremally disconnected. It is also shown that in an 𝑜𝑠-regular space 𝑋 if every point has an 𝑆𝐶𝑆 neighborhood, then 𝑋 is 𝑆𝐶𝑆.