Some types of generalized closed and generalized star closed sets in topological ordered spaces | ||
| Journal of Contemporary Technology and Applied Engineering | ||
| Volume 3, Issue 2, March 2025, Pages 13-15 PDF (400.35 K) | ||
| Document Type: Original Article | ||
| DOI: 10.21608/jctae.2024.313298.1034 | ||
| Author | ||
| VOLETY V S RAMACHANDRAM* | ||
| 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, ] = {yX / x y} and [ , x] = {yX / y x} are defined for any xX. 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). | ||
| Keywords | ||
| Increasing set; Decreasing set; Balanced set | ||
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