Title
IpOpen Sets,IpCont.,IpCon. and IpSep. axioms in topological spaces: Topological Spaces,Used
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In this work we introduce and study a new class of open sets by means of preopen that we call Ipopen set. By the above mentioned set, several new concepts such as Ipcontinuous functions, almost and weakly Ipcontinuous functions, Ipopen and Ipclosed functions, Ipconnected and Ipseparation axioms are defined and studied. In the light of this work, some of our main results can be listed as follows: If a space (X, t) is hyperconnected, then IpO(X) pO(X), and The following statements are equivalents for the function f: (X, t) (R) (Y, s): f is Ipcontinuous, the inverse image of every open set in Y is Ipopen set in X, the inverse image of every closed set in Y is Ipclosed set in X, for each AX, f (Ipcl(A)) clf (A), for each AX, intf (A) f (Ipint(A)), for each BY, Ipcl(f (B)) f (clB), for each BY and f (intB) Ipint(f (B)). Moreover let f: (X, t) (Y, s) be a function and let {A: } be preopen cover of X. If the restriction fA: A Y is Ipcontinuous function for each, then f is Ipcontinuous function. and also a function f: (X, t)(Y, s) is an Ip open function if and only if for every BY, f (Ip Cl (B)) Clf (B).
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