Geodesic
Strongly proximinal subspaces of finite codimension in $C(K)$
S. Dutta 1   ; Darapaneni Narayana 2
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
Colloquium Mathematicum, Tome 109 (2007) no. 1, pp. 119-128 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $C(K)$.
DOI : 10.4064/cm109-1-10
Keywords: characterize strongly proximinal subspaces finite codimension spaces applications results first metric projection strongly proximinal subspace finite codimension hausdorff metric continuous second strong proximinality transitive relation finite codimensional subspaces

S. Dutta  1   ; Darapaneni Narayana  2

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

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