Semi-open Sets and Semi-continuous Maps Relative to a Subbase

This paper first gives the definitions of β-semi-open sets and β-semi-close sets with the help of the interior and the closure relative to a subbase and it defines the conceptions of β-semi-interior and β-semi-closure.Furthermore,it studies their basic properties and mutual relations,and gives their equivalent characterizations.Finally,it introduces the definition of semi-continuous maps relative to a subbase,and gives its equivalent characterizations.