A note on the new set operator ψr
A. Atay and H. İ. Tutalar
Recently many published works made on local function used in ideal topological spaces can be found in related literature. "Semi Local Functions in Ideal
Topological Spaces", "Closure Local Functions", and "()p and ψp-Operator"
can be mentioned among such works those aim to define such functions.
In general, the researchers prefer using the generalized open sets instead of topology in ideal topological spaces. Obtaining a Kuratowski closure operator
with the help of local functions is an important detail in ideal topological space. However, it is not possible to obtain a Kuratowski closure operator from many
of these local functions proposed by the above mentioned works. In order to address the lack of such an operator, the goal of this paper is to introduce another
local function to give possibility of obtaining a Kuratowski closure operator. On the other hand, regular local functions defined for ideal topological spaces
have not been found in the current literature. Regular local functions for the ideal topological spaces has been described within this work. Moreover,
with the help of regular local functions Kuratowski closure operators
clI*r and τ*r topology are obtained. Many theorems in the literature have
been revised according to the definition of regular local functions.
Tbilisi Mathematical Journal, Vol. 11(4) (2018), 43-52