On ...-admissible Vector Space Topologies on C(X).
Let be the ring of real continuous functions on a completely regular Hausdorff space. In this paper an almost discrete space is determined by the algebraic structure of . The intersection of essential weak ideal in is also studied.
The concept of almost quasicontinuity is investgated in this paper in several directions (e.g. the relation of this concept to other generalizations of continuity is described, various types of convergence of sequences of almost quasicontinuous function are studied, a.s.o.).
A function is said to be almost quasicontinuous at if for each neighbourhood of . Some properties of these functions are investigated.
In this paper, we give an affirmative answer to the problem posed by Y. Tanaka and Y. Ge (2006) in "Around quotient compact images of metric spaces, and symmetric spaces", Houston J. Math. 32 (2006) no. 1, 99-117.