In this paper we study the classical notion of coproximinality, for quotient spaces of Banach spaces. We provide a partial solution to the three space problem, analogous to a classical result of Cheney and Wulbert, by showing that for , coproximinality of in and that of in implies the coproximinality of in , when is an -ideal in . For the space of continuous functions on a compact extremally disconnected set we derive the same conclusion under the assumption that is an -ideal in .
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T.S.S.R.K. Rao, Coproximinality for Quotient Spaces. Z. Anal. Anwend. 36 (2017), no. 2, pp. 151–157DOI 10.4171/ZAA/1583