ON PRE- T3/4 SPACES

Since every topological space is pre-T1/2 space, we aim to define a space that is weaker than pre-T1 space; namely pre-T3/4 space, when we use the notions of regular open sets and preopen sets. We prove that a pre-T3/4 space is weaker than T 3/4 space, regular space and pre-R space, additionally, we investigate the topological properties of pre-T3/4 space, as the hereditary property and their images by some paritcular functions; moreover we discuss the behavior of preT 3/4 axiom in some special spaces as; submaximal spaces, regular spaces, extremelly disconnected spaces and hyperconnected spaces.