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ON MAXIMAL, MINIMAL OPEN AND CLOSED SETS 1. Introduction
... 3. Maximal and minimal closed sets Definition 3.1 (Nakaoka and Oda [3]). A proper nonempty closed subset E of X is said to be a maximal closed set if any closed set which contains E is X or E. Theorem 3.2 (Nakaoka and Oda [3]). If E is a maximal closed set and F is any closed set, then either E ∪ F ...
... 3. Maximal and minimal closed sets Definition 3.1 (Nakaoka and Oda [3]). A proper nonempty closed subset E of X is said to be a maximal closed set if any closed set which contains E is X or E. Theorem 3.2 (Nakaoka and Oda [3]). If E is a maximal closed set and F is any closed set, then either E ∪ F ...
390 - kfupm
... called weakly BR-continuity. In this paper we define the notion of weakly BR-openness as a natural dual to the weakly BR continuity by using the notion of b-θ-open and b-θ-closed sets. We obtain several characterizations and properties of these functions. Moreover, we also study these functions comp ...
... called weakly BR-continuity. In this paper we define the notion of weakly BR-openness as a natural dual to the weakly BR continuity by using the notion of b-θ-open and b-θ-closed sets. We obtain several characterizations and properties of these functions. Moreover, we also study these functions comp ...
... Let K be a commutative ring with unity. An abelian group A which has a structure of both an associative ring and a K-module where the property λ(xy) = (λx)y = x(λy) is satisfied for all λ ∈ K and x, y ∈ A is called an associative algebra. We say that A is unital if it contains an element 1 such that ...
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... An Alexandroff space is a topological space in which arbitrary intersections of open sets are open. These spaces were first introduced by P. Alexandroff in 1937 in [1] under the name of Diskrete Räume. Finite spaces are a special case of Alexandroff spaces. There is a close relationship between Ale ...
... An Alexandroff space is a topological space in which arbitrary intersections of open sets are open. These spaces were first introduced by P. Alexandroff in 1937 in [1] under the name of Diskrete Räume. Finite spaces are a special case of Alexandroff spaces. There is a close relationship between Ale ...
normed linear spaces of continuous functions
... are linear forms a subset of S%- consisting of two disjoint homeomorphic images of X whose weak-* closures are disjoint sets in Sw homeomorphic to X. Now let X be the interval 2 1 / 2 - K ^ l , and let B be the set of luuctions^(^)=^2+^with||è||=supa;ex|ô(^)|.HereX=[21/2-l^x^l]. è ( 2 i / 2 - l ) = ...
... are linear forms a subset of S%- consisting of two disjoint homeomorphic images of X whose weak-* closures are disjoint sets in Sw homeomorphic to X. Now let X be the interval 2 1 / 2 - K ^ l , and let B be the set of luuctions^(^)=^2+^with||è||=supa;ex|ô(^)|.HereX=[21/2-l^x^l]. è ( 2 i / 2 - l ) = ...
Scattered toposes - Razmadze Mathematical Institute
... Statement 3. The relativized Kuroda Principle rKP is provable in the calculus QHC (and, hence, admits a provability interpretation). One possible approach to semantical analysis of the above calculi is via topos theory. It is well known that elementary toposes correspond to higher order intuitionist ...
... Statement 3. The relativized Kuroda Principle rKP is provable in the calculus QHC (and, hence, admits a provability interpretation). One possible approach to semantical analysis of the above calculi is via topos theory. It is well known that elementary toposes correspond to higher order intuitionist ...