The reflexivity of the category of stratified L-algebraic closure spaces

In this paper, for each commutative and integral quantale, we give the stratified Sierpinski L-algebraic closure space and a sobrification of stratified L-algebraic closure spaces. Furthermore, we show that \bf{S}L-\bf{AC}_۰---the category of stratified S_۰-L-algebraic closure spaces is epireflective in \bf{S}L-\bf{AC}---the category of stratified L-algebraic closure spaces, and \bf{Sob}L-\bf{AC}---the category of sober L-algebraic closure spaces is epireflective and \mathcal{E}-firm epireflective in the category \bf{S}L-\bf{AC}_۰.

کلیدواژه ها:

stratified L-algebraic closure space ، Sierpinski space ، sober ، epireflective