# subset

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Related to subset: Proper subset

## subset

Maths
a. a set the members of which are all members of some given class: A is a subset of B is usually written A⊂B
b. proper subset one that is strictly contained within a larger class and excludes some of its members.

## Subset

A subset of a set A is any set each of whose elements belongs to A. For example, the set of all even numbers is a subset of the set of all integers. If the empty set is included among the sets, then by definition it is a subset of any other set. The set A itself and the empty set are sometimes called improper subsets, while the other subsets are called proper.

## subset

[′səb‚set]
(communications)
A telephone or other subscriber equipment connected to a communication system, such as a modem. Derived from subscriber set.
(mathematics)
A subset A of a set B is a set all of whose elements are included in B.
A fuzzy set A is a subset of a fuzzy set B if, for every element x, the value of the membership function of A at x is equal to or less than the value of the membership function of B at x.

## subset

A group of commands or functions that do not include all the capabilities of the original specification. Software or hardware components designed for the subset will also work with the original. However, any component designed for the full original specification will not operate with the subset product. Contrast with superset.
References in periodicals archive ?
A neutrosophic subset A of a neutrosophic topological space (U, T) is called neutrosophic semi-[alpha]-open set (briefly NS[alpha]-OS) if there exists a N[alpha]-OS K in U such that K [subset or equal to] N [subset or equal to] ncl(H) or equivalently if A [subset or equal to] Ncl([alpha]Nint(A)).
1982), defined a subset A of (X,[tau]) is called pre-open locally dense or nearly open if A [subset] Int (Cl (A)) and its complement is called pre-closed set.
If K is a weakly compact subset of E and K with the relative weak topology is metrizable (for example E could be a Banach space whose dual [E.
The closure (smallest closed set containing F) of a subset F [subset or equal to] [X.
A subset A of a space (X, [tau], I) with an ideal I is said to be pre-I-regular if it is pre-I-open and pre-I-closed.
Let A be a gJ[lambda]-closed subset of (X, [lambda]).
The sets V [intersection] G, H [intersection] W [intersection] G and K [intersection] W [intersection] G are mutually disjoint open subsets of G containing p, q and x, respectively.
s,t)] | [there exists]u, v with f [not subset or equal to] [bar.
m]) be the space of all compact and convex subsets of [R.
The semi-closure [3] of a subset A of X, denoted by sCl(A), is defined to be the intersection of all semi-closed sets containing A in X.
Effector T cells belonging to both subsets were found in invasive disease.
A subset of a topological space is called [alpha] open if A is a subset of int cl int(A).

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