relative topology

relative topology

[′rel·əd·iv tə′päl·ə·jē]
(mathematics)
In a topological space X any subset A has a topology on it relative to the given one by intersecting the open sets of X with A to obtain open sets in A.
References in periodicals archive ?
Then, a neutrosophic relative topology on Y is defined by
is a neutrosophic relative topology on Y such that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Let TA be the relative topology on A , then A is [alpha]-[tau]-disconnected if and only if A is [alpha]-[tau]A -disconnected.
A topological space X is Lindelof if and only if X has a cover [{[X.sub.n]}.sup.[infinity].sub.1] such that subspaces [X.sub.n] under the relative topology, are all Lindelof.
If (X, T) constitutes a topological space, and Y is part of X, it is possible to build a topology [T.sub.Y] of Y called relative topology or relativization of T to Y.
For convenience, let [H.sub.i] = [H.sub.|Ii], the restriction of H on [I.sub.i], [T.sub.i] = [T.sub.|Ii], the relative topology on [I.sub.i], and ||*|| denote the supremum norm.
It is shown in [7] that the largest locally convex algebra (with respect to the relative topology induced by CV(X) and the pointwise multiplication) is