ON NEW LOCAL FUNCTION IN GRILL TOPOLOGICAL SPACE
DOI:
https://doi.org/10.59743/jbs.v39i1.342Keywords:
Additive property, Associated operator, Grill, Ideal, Semi-open setAbstract
The subject grill was introduced to obtain the deeper property of compactness. But in the paper “New Local Function in Grill Topological spaces published in Baghdad Science Journal”, the grill is used to determine the several topologies on a set. To obtain same, the authors used additive property of grill related local function. They have also considered the Levine's semi-open and their arbitrary union & finite intersection properties. Whereas the collection of semi-open sets does not hold the intersection property. It is a crucial part of semi-open set to obtain a topology with the help of the same collection. The grill is also not closed under finite intersections. In this point of view, we further consider semi-open sets and grill together to discuss the finite additivity property of the local function. We have shown that the additivity property does not hold in general by some counter examples. Thus, there are some incorrect methods to obtain several topologies have been discussed in the paper “New Local Function in Grill Topological spaces published in Baghdad Science Journal”: we have also given some ways to obtain the additive property of local function and hence determining the several topologies on the set.
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