# Wydawnictwa / Czasopisma IMPAN / Colloquium Mathematicum / Wszystkie zeszyty

## Strongly proximinal subspaces of finite codimension in $C(K)$

### Tom 109 / 2007

Colloquium Mathematicum 109 (2007), 119-128 MSC: 41A65, 46B20. DOI: 10.4064/cm109-1-10

#### Streszczenie

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 $C(K)$.

#### Autorzy

Ben Gurion University
P.O.B. 653
Beer-Sheva 84105, Israel
and
Stat Math Unit
Indian Statistical Institute
Kolkata, India
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