Certain properties of bicompactifications

Let P be some topological property. A space X is said to be P-situated in the bicompactification bX if in bX, X has a basis of open neighborhoods each of which possesses property P. In the class of normal and in the class of extremally disconnected spaces we give the intrinsic characteristics of spaces weakly paracompactly situated in their own Stone-Cech bicompactifications. We consider other applications of the concept of the P-situation of spaces in their bicompactifications.Translated from Matematicheskie Zametki, Vol. 17, No. 3, pp. 467–473, March, 1975.