\tau*-generalized semi continuous functions in topological spaces

On Τ*-Generalized PRE CONTINUOUS MULTIFUNCTIONS IN TOPOLOGICAL SPACES

“…[2] Definition: 2.12 A function F: X → Y from a topological space X into a topological space Y is called τ * -gcontinuous if the inverse image of a g-closed set in Y is τ * -gclosed in X. [5] Definition: 2.13 A function F: X → Y from a topological space X into a topological space Y is called τ * -gp continuous if the inverse image of every gp-open set in Y is τ * -gopen in X.…”

τ-Generalized Homeomorphism in Topological Spaces

“…Definition 2.4.. A topological space (X, τ*) is called τ*-T g space [6] if every τ*-g-closed set in X is g-closed in X. Definition 2.5.…”

“…is called τ*-generalized continuous [6] vi) quasi semiopen [15] if the image of each semiopen set in X is open set in Y.…”

“…Then f is both g-continuous map and g-open map. In [6], it has been proved in Theorem 3.6 that every g-continuous map is *-g-continuous. So, f is *-g-continuous.…”

“…Using the topology * introduced by Dunham [5], Pushpalatha et al [11] introduced * generalized closed sets and examined its properties. In [6], Eswaran and Pushpalatha defined the notion of  * -generalized continuous maps and a space called τ*-T g space. Using generalized closed sets, Balachandran et al [1] introduced and studied the notion of generalized continuous maps.…”