# Coproximinality for Quotient Spaces

### T.S.S.R.K. Rao

Indian Statistical Institute, Bangalore, India

## Abstract

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 Z \subset Y \subset X, coproximinality of $Z$ in $X$ and that of $Y/Z$ in $X/Z$ implies the coproximinality of $Y$ in $X$, when $Z$ is an $M$-ideal in $X$. For the space $C(K)$ of continuous functions on a compact extremally disconnected set $K$ we derive the same conclusion under the assumption that $Z$ is an $M$-ideal in $Y$.

## Cite this article

T.S.S.R.K. Rao, Coproximinality for Quotient Spaces. Z. Anal. Anwend. 36 (2017), no. 2, pp. 151–157

DOI 10.4171/ZAA/1583