# closed set

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Related to Closed sets: Bounded set

## closed set

n
1. (Mathematics) a set that includes all the values obtained by application of a given operation to its members
2. (Mathematics) (in topological space) a set that contains all its own limit points
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References in periodicals archive ?
Proof: - since A and B are disjoint closed sets in compact Hausdorff space W(X, G), then there are open sets [O.sub.1] and [O.sub.2] such that A [subset] [O.sub.1] [subset] [[bar.O].sub.1], B [subset] [O.sub.2] [subset] [[bar.O].sub.2] and [[bar.O].sub.1][intersection] [[bar.O].sub.2] = [phi] since G separates closed sets, there are sets [G.sub.1] [G.sub.2] [member of] G such that [[bar.O].sub.1] [subset] [[bar.G].sub.1], [[bar.O].sub.2] [subset] [[bar.G].sub.2] and [[bar.G].sub.1] [intersection] [[bar.G].sub.2] = [phi].
Morgan builds the theory behind calculus from the basic concepts of real numbers, limits, and open and closed sets, and includes proofs and exercises for the undergraduate student.
Salama et al., [4,1, 2] introduced the generalization of neutrosophic sets, neutrosophic crisp sets and the neutrosophic closed sets in the field of neutrosophic topological spaces.
In this paper, we introduce the concept of [[alpha].sub.[gamma]]-open sets by using an operation [gamma] on [alpha]O(X, [tau]) and we introduce the concept of [[alpha].sub.[gamma]]-generalized closed sets and [[alpha].sub.[gamma]]-[T.sub.1/2] spaces and characterize [[alpha].sub.[gamma]]-[T.sub.1/2] spaces using the notion of [[alpha].sub.[gamma]]-closed or [[alpha].sub.[gamma]]-open sets.
A space X is said to be vg-normal if for any pair of disjoint closed sets [F.sub.1] and [F.sub.2], there exist disjoint vg-open sets U and V such that [F.sub.1] [subset] U and [F.sub.2] [subset] V
The elements of the [sigma]-algebra generated by zero-sets are called Baire sets and the elements of the [sigma]-algebra generated by closed sets are called Borel sets; B(X)and [B.sub.0](X) are the classes of Borel and Baire subsets of X and [M.sub.[sigma]](X) denotes the class of all scalar-valued, countably additve Baire measures on X.
Regular generalized closed sets. Kyungpook Math J., 33 : 211-219.
The scope of this paper is to offer an overview of the main results obtained by the authors in recent literature in connection with the introduction of a Delta formalism, a la Dirac-Schwartz, for random generalized functions (distributions) associated with random closed sets, having an integer Hausdorff dimension n lower than the full dimension d of the environment space [R.sup.d].
(ii) The intersection of any number of neutrosophic soft cubic closed sets is a neutrosophic soft cubic closed set over X.
Benchalli and Wali [4] introduced the concept of regular weakly closed sets in 2007.
The complements of the above mentioned closed sets are their respective open sets.
Moreover, we introduced new types of open and closed sets in the context of [N.sub.nc]-topological spaces.

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