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strong topology

   Also found in: Wikipedia 0.01 sec.
strong topology [′strȯŋ tə′päl·ə·jē]
(mathematics)
The topology on a normed space obtained from the given norm; the basic open neighborhoods of a vectorxare sets consisting of all those vectorsywhere the norm ofx-yis less than some number.


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2](M', [gamma]) endowed with the inductive limit topology which coincides with the strong topology.
]) is said to be strongly complete in the strong topology if and only if every strongly Cauchy sequence in V is strongly convergent to a point in V.
[PHI] (n times) and the convergence is in [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (N') with respect to the strong topology.
 
 
 
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