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trivial topology

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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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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There exist [t.sub.1], ..., [t.sub.n] [member of] [GAMMA] such that for each t [member of] [GAMMA]\{[t.sub.1], ..., [t.sub.n]}, [X.sub.t] has trivial topology, moreover for each t [member of] {[t.sub.1], ..., [t.sub.n]}, [X.sub.t] is Alexandroff.
More about functional Alexandroff topological spaces
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