Generalized Urysohn spaces

Generalized Urysohn spaces are defined by using the concepts of semi-open and pre-open set instead of open set. A subset a topological space A of (X,τ) is said to be semi-open if there exists an open set U in X such that U⊆A⊆U ̅ and also A is pre-open if A⊆(A ̅ )^∘ . The complements of semi-open sets (pre-open) are called semi-closed (pre-closed). The main goals of this thesis are as follows: 1. To define and examine the spaces called semi-Urysohn, s-Urysohn, pre-Urysohn, and p-Urysohn spaces by using the concepts of semi-open sets and pre-open sets, 2. To determine the hereditariness ve productivity of generalized Urysohn spaces, 3. To investigate situations of generalized Urysohn spaces under new mappings such as semi-continuity, pre-continuity, θ-continuity, θ-irresolute, θ-pre-irresolute obtained using semi-open and pre-open concepts.