Total negation is a procedure, first formulated by Bankston in 1979, for generating from any given topological property P another (denoted by anti(P)) that is, in a precisely defined sense, ``the opposite property''. Iteration of the procedure generates a succession of properties that becomes repetitive in one of only seven patterns. Recent investigations have shown that when the procedure is constrained to take place within some fixed family (the ``constraint'') of spaces, this simple iterative behaviour can in general be lost, but not if the constraint satisfies some simple and natural hypotheses. This note focusses on how the patterns of repetition, under constraint and in the unconstrained (``universal'') setting, are related to one another for an arbitrary initial invariant. For completeness we begin with a fairly full outline of relevant previous results (without proofs: which will be found in the references).
This article was published in a revised form. T. B. M. McMaster\ and\ C. R. Turner, Total negation under constraint: pre-anti properties. Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8) {\bf 3} (2000), no.~2, 367--374; MR 2001i:54007
Date received: December 18, 2000.