i-Semi-Inter-Open Sets in Topological Spaces

This work introduces a novel class of  sets are called -semi-inter open sets and semi-inter open sets in topological spaces. A number of mathematical arguments have been used to thoroughly examine some of these sets' characteristics and their connections to other kinds of sets, including, for example we proved that in any topological space   : Each  is semi inter open set and semi-inter open set, each set is semi-inter open set and semi inter open set, each semi inter open set is -open set and semi inter open set, each open set is semi inter open set and semi inter open set, however, generally speaking the converses are not necessary to be valid. Also, we defined the topologically extended and non-topologically extended property for -semi-inter sets, and we show that the family of -semi inter open sets is not necessarily a topological space, with some characterizations as -semi-inter limit points, -semi-inter boundary of a set.