generalezed cloesed

Definition

• A subset A of a space (X,) is called a generalized closed set (briefly, g－closed) if cl(A) ⊂ U whenever A ⊂ U and U is open. The complement of a g－closed set is called a g－open set.

Property

• closed → g－closed → rg－closed?.
• g-closed → gp-closed?.
• g-closed → gs-closed?.
• g-closed → πg-closed?.

Rerference

• Levine, Norman, Generalized closed sets in topology., Rend. Circ. Mat. Palermo (2) 19 (1970), 89–96.