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finite character[′fī‚nīt ′kar·ik·tər]
A property of a family C of sets such that any finite subset of a member of C belongs to C, and C includes any set all of whose finite subsets belong to C.
A characteristic of a property of subsets of a set such that a subset S has the property if and only if all the nonempty finite subsets of S have the property.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.