1Department of Mathematics Ben Gurion University P.O.B. 653 Beer-Sheva 84105, Israel and Stat Math Unit Indian Statistical Institute Kolkata, India 2Department of Mathematics Indian Institute of Science Bangalore 560012, India
Colloquium Mathematicum, Tome 109 (2007) no. 1, pp. 119-128
We characterize strongly proximinal subspaces of finite codimension in $C(K)$ spaces. We give two applications of our results. First, we show that the metric projection on a strongly proximinal subspace of finite codimension in $C(K)$ is Hausdorff metric continuous. Second, strong proximinality is a transitive relation for finite-codimensional subspaces of $C(K)$.
1
Department of Mathematics Ben Gurion University P.O.B. 653 Beer-Sheva 84105, Israel and Stat Math Unit Indian Statistical Institute Kolkata, India
2
Department of Mathematics Indian Institute of Science Bangalore 560012, India
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S. Dutta; Darapaneni Narayana. Strongly proximinal subspaces of finite
codimension in $C(K)$. Colloquium Mathematicum, Tome 109 (2007) no. 1, pp. 119-128. doi: 10.4064/cm109-1-10
