On P-covering Dimension
by
Alias B. Khalaf
Departement of Mathematics, University of Dohuk,Dohuk, Kurdistan Region, Iraq

In this paper, we introduce a covering dimension in general topological spaces by using pre open sets instead of open sets in the definition of the classical covering dimension, the concept of pre open sets in topological space was introduced in 1983. We define the p-covering dimension as follows: If X is any topological space, the p-covering dimension of X(p-dimX) is -1 if X is empty and we say that p-dimX is less than or equal to n if each finite p-open covering of X has a p-open refinement of order not exceeding n, if no such n exists we shall say that p-dimX is infinity. It is clear that p-dimX is different from dimX . Any topological space X in which the members of its topology are X, the empty set and a singleton, then dimX=0 but p-dimX(>0) is greater than zero. We proved some results on p-dim and give some characterizations on other spaces.

Some References:

1)Pears A R, Dimension Theory of general spaces, Queen Elezabeth College, London University.

2)A.S. Mashhour, M.E. Abd El-Monsef and S.N. El-Deeb, On pretopological spaces, Bull. Math. de la Soc. R.S. de Roumanie 28(76) (1984), 39-45.

3) I.L. Reilly and M.K. Vamanamurthy, On some questions concerning preopen sets, preprint.

Date received: November 10, 2005