[PDF] Top 20 Minimal closed sets and maximal closed sets
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Minimal closed sets and maximal closed sets
... The symbol Λ \ Γ means di ff erence of index sets, namely, Λ \ Γ = Λ − Γ , and the cardi- nality of a set Λ is denoted by | Λ | in the following arguments. A subset M of a topological space X is called a pre-open ... See full document
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Generalized Maximal Closed Sets in Topological Space
... of closed set is fundamental in the study of topological ...generalized closed sets in topological spaces by comparing the closure of a subset with its open ...g-closed sets was ... See full document
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A NEW CLASS OF MINIMAL AND MAXIMAL SETS VIA BĜ – CLOSED SET
... Recently minimal open sets and maximal open sets in topological spaces were introduced and studied by ...of sets called bĝ–minimal and bĝ–maximal closed sets ... See full document
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Generalized Minimal Closed Sets in Bitopological Spaces
... bitopological space. Kelly [5] initiated the systematic study of such spaces. After the work of Kelly [5] various authors [2,3,7,8] turned their attention to generalization of various concepts of topology by considering ... See full document
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Minimal and Maximal Soft Open Sets
... On the other hand, the notation of maximal open sets and minimal open sets were introduced by F. Nakaoka and N. Oda in [3] and [4] . Many generalizations of these concepts have been introduced ... See full document
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m*-Operfect Sets and $\alpha$-m*-Closed Sets
... ideal minimal spaces ...regular closed sets. In [7] Maki introduced the notions of minimal structures and minimal ...between sets, satisfying some minimal ...ideal ... See full document
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Closed Sets for Labeled Data
... of closed itemsets obtained from data from Table ...the closed set occurs. Notice that all closed itemsets with the same support cover a different subset of transactions of the original ...of ... See full document
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Indexed Enhancement on GenMax Algorithm for Fast and Less Memory Utilized Pruning of MFI and CFI
... mining maximal frequent item ...possible closed frequent item sets and construct an index for each MFI and CFI generated for fast and less memory utilized pruning of frequent item ... See full document
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Igm - Closed Sets
... − closed set [6] if cl(A) ⊂ U whenever A ⊂ U and U is ...− closed set. A sub collection M of P (X) is called a minimal structure [1] on X , if (i) φ, X ∈ M and (ii) M is closed under finite ... See full document
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W R0 Space in Minimal G Closed Sets of Type1
... spaces in topological ordered spaces in 2014. G.Venkareswarlu, V.Amarendra Babu, and M.K.R.S Veera kumar [11] introduced and studied minimal open sets of Type1 sets, minimal g-open sets ... See full document
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On Minimal and Maximal Regular Open Sets
... is minimal open, but not minimal regular open and the set {b, d} is min- imal regular open, but not minimal ...is maximal regular open, but not maximal open and the set {a, b, c} is ... See full document
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On θ generalized closed sets
... Clearly, every TGO-connected space is connected. The space in [3, Ex. 11] shows that there are connected spaces which are not TGO-connected. Since every θ-generalized closed set is g-closed, every ... See full document
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On generalized ω closed sets
... Proof. We need to show the sufficiency part only. Let x ∈ X and suppose that { x } is not closed. Then A = X − { x } is not open, and thus A is gω-closed (the only open set con- taining A is X). Therefore, by ... See full document
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Supra*g-Closed Sets in Supra Topological Spaces
... . Since F C is supra -open set and A is supra*g-closed, cl μ (A) ⊆F C . That is, F ⊆ (cl μ (A)) C . Hence F ⊆cl μ (A)∩[cl μ (A)] C =φ .That is, F=φ. Thus cl μ (A)\A contains no nonempty supra -closed set. ... See full document
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Application of αδ Closed Sets
... X X . Assume that a sequence x n is αδ-converging to x and y . Then it follows that x x n , n αδ-converges to x y , . By hypothesis, since Δ is sequentially αδ- closed, we have x y , . ... See full document
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Operation on $lak$-closed sets
... open sets play a vital role in research area of General ...open sets in ...semi-open sets to define the notion of semi-generalized closed ...of sets and studied the con- cept of ... See full document
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G-Nαg Closed Sets and G-Ngα Closed Sets in Grill Nano Topological Spaces
... Proof: i) G-Nα g-cl(A)= ∩{C:A⊆ C, C is G-Nα g-closed} X-G- Nα gcl(A) = X-∩{C:A⊆C, C is G-Nα gclosed} =∪ {X-C: A⊆ C, C is a G-Nα g -closed} =∪ {U: U⊆ X-A is GNα g -open} =G-Nα g-int(X-A) ... See full document
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On -closed sets in bitopological spaces
... In the present paper we introduce the concept of g ˆˆ -closed sets [12] in bitopological spaces and then investigate some of their properties. We also define and study new types of spaces namely T ˆˆ 1/ 2 ... See full document
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δ − Ig - Closed Sets
... Proof. (a) ⇒ (b). Let x ∈ X. If { x } is not closed, then X is the only open set containing X − { x } and hence X − { x } is δ − g − closed. By hypothesis, X − { x } is ? − closed. Therefore, { x } ... See full document
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On gγ-τ-Connectedness and gγ-τ Disconnectedness in Topological Spaces
... [11] J.A.Guthrie, H.E.Stone and M.L.Wage, Maximal connected expansions of the reals, Proc. Amer. Math. Soc., 69 (1) (1978) 159-165. [12] J.A.Guthrie, D.F.Reynolds and H.E.Stone, Connected expansions of topologies, ... See full document
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