trivial topology

(redirected from Indiscrete topology)

trivial topology

[¦triv·ē·əl tə′päl·ə·jē]
(mathematics)
For a set S, a topology whose only members are the set itself and the empty set. Also known as indiscreet topology.
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For this purpose, we introduce a natural topology on Milnor's K-groups [K.sup.M.sub.l](k) for a topological field k as the quotient topology induced by the joint determinant map and show that, in case of k = R or C, the natural topology on [K.sup.M.sub.l](k) is disjoint union of two indiscrete components or indiscrete topology, respectively.
If (X, [tau], E) is a soft topological space with [tau] = {[PHI], [??]}, then t is called the soft indiscrete topology on X and ([PHI], [tau], E) is said to be a soft indiscrete topological space.
This topology is called the indiscrete topology. The discrete topology of IFRSs in X contains all the IFRSs in X.