Strictly convex norms, $G_\delta$-diagonals and non-Gruenhage spaces
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- by Richard J. Smith PDF
- Proc. Amer. Math. Soc. 140 (2012), 3117-3125 Request permission
Abstract:
We present an example in ZFC of a locally compact, scattered Hausdorff non-Gruenhage space $D$ having a $G_\delta$-diagonal. This means that Gruenhage spaces are not necessary for the construction of strictly convex dual norms on dual Banach spaces, answering a question posed by Orihuela, Troyanski and the author. In addition, we show that the Banach space of continuous functions $C_0(D)$ admits a $C^\infty$-smooth bump function.References
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Additional Information
- Richard J. Smith
- Affiliation: School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland
- Email: richard.smith@ucd.ie
- Received by editor(s): February 4, 2011
- Received by editor(s) in revised form: March 21, 2011
- Published electronically: January 4, 2012
- Communicated by: Thomas Schlumprecht
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 3117-3125
- MSC (2010): Primary 46B03, 54G12
- DOI: https://doi.org/10.1090/S0002-9939-2012-11142-6
- MathSciNet review: 2917084