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A note on monolithic scattered compacta

Jesús Ferrer

subject

Pure mathematicsDual unitApplied MathematicsFirst-countable spaceMathematical analysisBanach spaceLocally compact spaceBall (mathematics)AnalysisSeparable spaceMathematics

description

Abstract For a Banach space E, it is well-known that a necessary condition for E to have the controlled separable complementation property (CSCP, for short) is that the dual unit ball B E ⁎ be monolithic in the weak-star topology. We prove here that when X is a scattered first countable locally compact space, then monolithicity of X turns out to be sufficient for C 0 ( X ) to enjoy the CSCP.

yearjournalcountryeditionlanguage
2015-01-01Journal of Mathematical Analysis and Applications
https://doi.org/10.1016/j.jmaa.2014.07.011