approximation property

approximation property

[ə‚präk·sə′mā·shən ‚präp·ərd·ē]

(mathematics)

The property of a Barach space, B, in which compact sets are approxiately finite-dimensional in the sense that, for any compact set, K, continuous linear transformations, L, from K to finite-dimensional subspaces of B can be found with arbitrarily small upper bounds on the norm of L (x) -x for all points x in K.

McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.