If not distinguished, is $C_{p}( X) $ even close?

نویسندگان

چکیده

$C_{p}\left ( X\right )$ is distinguished $\Leftrightarrow$ the strong dual $L_{\beta }\left barrelled bidual $M\left ) =\mathbb {R}^{X}$. So one may judge how nearly by is, and also near dense subspace to Baire space $\mathbb Being Baire-like, always fairly close {R}^{X}$ in that sense. But if not distinguished, we show codimension of uncountable, i.e., algebraically far from {R}^{X}$, moreover, very barrelled, even primitive. Thus profile weak barrelledness for spaces. At same time, characterize those Tychonoff spaces $X$ which solving original problem our series papers.

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ژورنال

عنوان ژورنال: Proceedings of the American Mathematical Society

سال: 2021

ISSN: ['2330-1511']

DOI: https://doi.org/10.1090/proc/15439