Complementation in spaces of continuous functions on compact lines

Abstract

We characterize order preserving continuous surjections between compact linearly ordered spaces which admit an averaging operator, together with estimates of the norm of such an operator. This result is used to the study of strengthenings of the separable complementation property in spaces of continuous functions on compact lines.

These properties include in particular continuous separable complementation property and existence of a projectional skeleton.

Keywords

• Compact linearly ordered space
• Averaging operator
• Continuous separable complementation property
• Projectional skeleton