# open set

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Related to open set: Closed set, Connected set

## open set

n
1. (Logic) a set which is not a closed set
2. (Mathematics) an interval on the real line excluding its end points, as [0, 1], the set of reals between, but excluding, 0 and 1
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014
References in classic literature ?
Those who remarked in the physiognomy of the Prince a dissolute audacity, mingled with extreme haughtiness and indifference to, the feelings of others could not yet deny to his countenance that sort of comeliness which belongs to an open set of features, well formed by nature, modelled by art to the usual rules of courtesy, yet so far frank and honest, that they seemed as if they disclaimed to conceal the natural workings of the soul.
The concepts of Intuitionistic Fuzzy Exponential Map Via Generalized Open Set by Dhavaseelan et al[8].
(1) A is said to be [[tau].sub.1]-[delta] open set, if, for x [member of] A, there exists [[tau].sub.12]-regular open set G such that x [member of] G [subset] A.
Keywords: Semi open set, semi closed set, irresolute mapping, semi homeomorphism, irresolute topological group, semi connected space, semi component, semi topological groups with respect to irresoluteness.
Clearly cl((F, A)) is the smallest soft closed set over X which contains (F, A) and int((F, A)) is the largest soft open set over X which is contained in (F, A).
Recall that a [T.sub.0]-topology is a topology satisfying the separate axiom: for all x [not equal to] y, there is an open set containing one but not the other.
Clearly cl(A, E) is the smallest soft closed set over X which contains (A, E) and int(A, E) is the largest soft open set over X which is contained in (A, E).
A subset A of X with an operation [gamma] on [tau] is called [gamma]-open (OGATA, 1991) if for each x [member of] A, there exists an open set U such that x [member of] U and [gamma](U) [subset or equal to] A.
A set A in a topological space (X,T) is semi-open, denoted by A[member of] SO(X,T), iff there exists an open set O such that O[subset or equal to] A[subset or equal to] Cl(O).
Then, sg-Int([f.sup.-1](G)) is a sg- open set in X and f is quasi sg-open, then f (sg-Int([f.sup.-1](G))) [subset] Int(f ([f.sup.- 1](G))) [subset] Int(G).
holds for every open set U and any two subspaces A, B of X.

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