Год выпуска: 2012
Автор: Diyar Muhsen and Layla Saadulla
Издательство: LAP Lambert Academic Publishing
Страниц: 124
ISBN: 9783838390024
Описание In this work we introduce and study a new class of open sets by means of preopen that we call Ip-open set. By the above mentioned set, several new concepts such as Ip-continuous functions, almost and weakly Ip-continuous functions, Ip-open and Ip-closed functions, Ip-connected and Ip-separation 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, ?) is hyperconnected, then IpO(X) pO(X), and The following statements are equivalents for the function f: (X, ?) ® (Y, ?): f is Ip-continuous, the inverse image of every open set in Y is Ip-open set in X, the inverse image of every closed set in Y is Ip-closed set in X,for each AIX, f (Ipcl(A))I clf (A), for each AIX, intf (A) I f (Ipint(A)), for each BIY, Ipcl(f ?? (B))I f ?? (clB), for each BIY and f ?? (intB)I Ipint(f ?? (B)). Moreover let f: (X, ?) --(Y, ?) be a function and let {A : } be pre-open cover of X. If the restriction f|A :A ?Y is Ip-continuous... |
