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The Kannai and closed-convergence topologies on spaces of continuous preferences are modeled to prove their coincidence under spaces of economic preference. Their characterization lead to the questionnaire topology which, in contrast to the two, is not constrained to continuous preferences so long as there are other assumptions. This equivalent topology also lends itself to easy verification of denseness results.

In this paper we relax the unrestricted domain condition of Arrow's Impossibility Theorem to allow the consideration of domains of econimic preferences--i.e., continuous monotonic preferences on some positive orthant [R.sup.M.sub.+]. The impossibility result remains in effect after all but the most drastic reductions in the size of the domain, in the sense that any domain admitting an Arrow SWF must be nowhere dense in the usual topology on the set of admissible preference profiles.