We study on cofinitely (strong) refinable modules as a proper generalization of (strongly) refinable modules. In this paper various properties of these modules are developed. It is shown that (1) every (cofinite) direct summand of a (cofinitely) refinable module is (cofinitely) refinable; (2) a module is cofinitely refinable if and only if every cofinite direct summands lift modulo every submodule of ; (3) a ring  is Rad-supplemen-ted and left refinable if and only if it is semiperfect; (4) a semilocal ring  is a left and right artinian serial ring with  if and only if every left -module is strongly refinable.
 2010 Mathematics Subject Classification. 16D10,16D40.
Key words and phrases. (strongly) refinable module, Â cofinitely (strong) refinable module, semiperfect ring
The main objective of this paper is to study the notions of Minimal m-GS Closed set, Maximal m-GS Open set, Minimal m-GS Open set and Maximal m-GS Closed set and their basic properties in Minimal Space.
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Key Words: GS-closed set, Minimal GS-closed set, Maximal GS-closed set, GS-open set, Minimal GS-open set, Maximal GS-open set
In this paper we introduce and investigate the notions of â„gr*-closed sets and â„gr*-continuous functions, maximal â„gr*-closed sets and Maximal â„gr*-continuous functions in ideal topological spaces.
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Keywords: â„gr*-closed sets, â„gr*-continuous functions, maximal â„gr*-closed sets, Maximal â„gr*-continuous functions.