relative topology

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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 ?
The set of all homomorphisms hom(G, U(H)) can be endowed with the subspace topology of the compact-open topology of the space
Definition 7 A subspace (Eq.) of a topological space (Eq.) is semi connected [6], if it is semi connected in the subspace topology. i.e if there do not exist disjoint semi open sets (Eq.) and (Eq.) of (Eq.) , such that (Eq.).
Then (P, T) is called a subspace topology of (X, [tau]).
([??]): Suppose T \ A is not dense in T when T equipped with the subspace topology, then there exists a non-empty open set O [member of] [OMEGA(T), O [subset or equal to] A.
Hence, there exists an n-dimensional subspace Z of Y (equipped with the subspace topology) with basis {[e.sub.1]...
Then [[tau].sub.M] = {[[phi].sub.M], [1.sub.M], [M.sub.1], [M.sub.2], [M.sub.3]} is neutrosophic soft subspace topology on (U, E).
Then (P,T) is called a subspace topology of (X,[tau]).
Restricted interval valued neutrosophic subspace topology is also studied.
5 Interval Valued Neutrosophic Soft Subspace Topology
interval valued fuzzy neutrosophic soft subspace topology (IVFNS subspace topology) and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is called interval valued fuzzy neutrosophic soft subspace of (([F.sub.A], E), [tau]).
Consider on A x C the product topology induced by the topologies of A and C and consider on D the subspace topology [[tau].sub.D] induced by the product topology on A x C.
Then the collection [[tau].sub.y] = {(Y, E) [intersection] (Q, E) : (Q, E) [member of] [tau]} is called a neutrosophic soft cubic subspace topology on (X,E).