In this article let us prepare the background of the
subject. Throughout this paper, stands for
topological space. Let be a subset of . A point in is
called condensation point of if for each in with in
, the set U is uncountable [2]. In 1982 the closed
set was first introduced by H. Z. Hdeib in [2], and he
defined it as: is closed if it contains all its
condensation points and the open set is the
complement of the closed set. It is not hard to prove:
any open set is open. Also we would like to say that
the collection of all open subsets of forms topology
on . The closure of will be denoted by , while the
intersection of all closed sets in which containing
is called the closure of , and will denote by .
Note that .
In 2005 M. Caldas, T. Fukutake, S. Jafari and T.
Noiri [3] introduced some weak separation axioms by
utilizing the notions of open sets and
closure. In this paper we use M. Caldas, T.
Fukutake, S. Jafari and T. Noiri [3] definitions to
introduce new spaces by using the open sets defined
by H. Z. Hdeib in [3], we ecall it Spaces
, and we show that , space
and symmetric space are equivalent.
For our main results we need the following