In this work, we introduce and study new types of slightly continuous function namely (slightlysgb-continuous and slightly s*gb-continuous) functions in topological spaces .Also, we will be investigate anddiscussion the relationships between these functions with some other types of slightly continuous functionsFurthermore, we will be study and proved some of their properties.Keyword : Slightly continuous, slightly pre-continuous, slightly semi- continuous, sgb-continuous
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