Some types of generalized closed and generalized star closed sets in topological ordered spaces

Document Type : Original Article

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V.V.S.RAMACHANDRAM D.NO 1-59 SRINIVASA NAGAR KATHERU RAJAHMUNDRY RURAL

Abstract

The notion of topological ordered space was first studied by L. Nachbin [9]. A triple (X, , ) where X is a non-empty set, is a topology and is a partial order on X called as a topological ordered space. A subset A of topological ordered space (X, , ) is said to be an increasing set if A = i(A) and is a decreasing set if A = d(A) where and .The sets [x, ] = {yX / x  y} and [ , x] = {yX / y  x} are defined for any xX. The complement of an increasing set is a decreasing set and vice versa. A subset of a topological ordered space (X, , ) is a balanced set if it is both increasing and decreasing set.In the present work our intention is to establish relationship between new types of closed sets namely g*b-closed sets (resp.gb-closed) and g*i-closed sets(resp.gi-closed) and g*b-closed sets(resp.gb-closed) and g*d-closed sets(resp.gd-closed). We also established the independency between the notions g*i-closedness (resp.gi-closedness) and g*d-closedness (resp.gd-closedness).

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