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Semi-open Sets and Semi-Continuity in Topological Spaces

Semi-open Sets and Semi-Continuity in Topological Spaces,N. Levine

Semi-open Sets and Semi-Continuity in Topological Spaces   (Citations: 249)
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Published in 1963.
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    • ...semiopen [14], b-open [2], α-open [17], β-open [1]) set if A int cl A (resp...

    Erdal Ekiciet al. New generalized topologies on generalized topological spaces due to Cs...

    • ...A subset A of X is said to be semi-open [32] (resp...
    • ...Definition 2.5. A function f :( X, τ) → (Y, σ )i s said to besemi-continuous [32] (resp...

    Takashi Noiriet al. A unified theory of weak contra-continuity

    • ...A subset A of a topological space (X, τ) is called preopen [24] (resp., semiopen [18], δ-preopen [32], δ-semiopen [28], α-open [27], β-open [1], b-open [4]) if A int cl (A) (resp., A cl int (A) , A int (clδ A), A cl (intδ A), A int (cl int (A) ), A cl int (cl A) , A cl int (A) ∪ int cl (A) ). A point x ∈ X is called a semi-θ-cluster point [22 ]o f as etA if scl U ∩ A � ∅ ,f or each semiopen set U containing x. The set of all semi-θ-cluster ...

    T. Noiriet al. Unification of generalized open sets on topological spaces

    • ...Continuity points of quasicontinuous mappings were studied in many papers; see for example Bledsoe [5], Hol´ a, Piotrowski [21], Kenderov, Kortezov, Moors [26], Levine [27], see also a survey paper of Neubrunn [34]...

    Dušan Holýet al. Quasicontinuous functions, minimal usco maps and topology of pointwise...

    • ...Definition 2.1. A subset A of a topological space (X, τ )i s said to be (1) semi-open [17] if A ⊂ Cl Int (A) , (2) preopen [20] if A ⊂ Int Cl (A) , (3) α-open [25] if A ⊂ Int (Cl Int (A) ), (4) b-open [5] if A ⊂ Cl Int (A) ∪ Int Cl (A) , (5) β-open [1] or semi-preopen [4] if A ⊂ Cl (Int Cl (A) )...
    • ...semi-continuous [17], precontinuous [20], αcontinuous [21], b-continuous [5] or γ-continuous [11], β-continuous [1] or semi-precontinuous [4])...

    T. Noiriet al. On decompositions of continuity in topological spaces

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