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Let ϊ°° be the algebra of all bounded sequences of complex numbers. The primary purpose of this paper is to settle, by means of a counter-example, a conjecture about subalgebras of l°°: If A is a subalgebra of l°° which is closed under uniform convergence and separates the points of βN, then A = l°°.doi:10.2140/pjm.1965.15.1239 fatcat:bzmdzptk6nbd7ma3z2dkyyxwey