Open Set


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Related to Open Set: Closed set, Connected set

open set

[′ō·pən ‚set]
(mathematics)
A set included in a topology; equivalently, a set which is a neighborhood of each of its points; a topology on a space is determined by a collection of subsets which are called open.

Open Set

 

a point set that does not contain the limit points of its complement. Every point of an open set is an interior point, that is, it has a neighborhood entirely contained in the open set. Together with closed sets, open sets play an important role in the theory of functions, in topology, and in other branches of mathematics. Any nonempty open set on a line is an open interval or a sum of an at most countable number of open intervals.

The concept of open set can be applied in an n-dimensional Euclidean space and also in an arbitrary metric or topological space. The intersection of a finite number of open sets is an open set, as is the union of any number of open sets. Connected open sets are called domains. Any topological space can be defined by specifying its open sets. If a topological space is given by a system of its closed sets, then the open sets are defined in it as the complements of the closed sets.

References in periodicals archive ?
Nint(A) = [union] {G | G is a neutrosophic open set in X and G [subset or equal to] A} is called the neutrosophic interior of A;
A subset of a topological space is said to be semi open, if there exists an open set in such that (Eq.
1] f(p)): p [member of] X} is a decomposition of (X,T) into closed, open sets, and (d) for each p [member of] X, there exists a closed, open set U containing p on which f is constant.
As Vy is a neighbourhood of y, there exists an open set Wy in Y such that y [member of] Wy [subset] Vy .
Then every open set of X is regular open if and only if every open set is closed.
Notice that each basic open set in T is the union of the images through the [f.
The concept of intuitionistic fuzzy semi-supra open set was introduced by Parimala and Indirani [7].
The aim of this paper is to introduce a new concepts of fuzzy of Intuitionistic fuzzy -strongly semi open set of a nonempty set and define an Intuitionistic fuzzy -strong semi continuity and Intuitionistic fuzzy -strongly semi retract.
2]) is (i, j)-weakly b-continuous if and only if for every open set V in Y, [f.
ii) v-open [resp: vg-open] if the image of open set is v-open [resp: vg-open].
He defined a set A in a topological space to be semi-open if there exists an open set O such that O [subset or equal to] A [subset or equal to] [bar.

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