The projective $\pi$-character bounds the order of a $\pi$-base
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- by István Juhász and Zoltán Szentmiklóssy PDF
- Proc. Amer. Math. Soc. 136 (2008), 2979-2984 Request permission
Abstract:
All spaces below are Tychonov. We define the projective $\pi$- character $p \pi \chi (X)$ of a space $X$ as the supremum of the values $\pi \chi (Y)$ where $Y$ ranges over all (Tychonov) continuous images of $X$. Our main result says that every space $X$ has a $\pi$-base whose order is $\le p \pi \chi (X)$; that is, every point in $X$ is contained in at most $p \pi \chi (X)$-many members of the $\pi$-base. Since $p \pi \chi (X) \le t(X)$ for compact $X$, this is a significant generalization of a celebrated result of Shapirovskii.References
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Additional Information
- István Juhász
- Affiliation: Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, POB 127, Budapest, H-1364 Hungary
- Email: juhasz@renyi.hu
- Zoltán Szentmiklóssy
- Affiliation: Department of Analysis, Eötvös Loránt University, Pázmány Péter sétány 1/A, 1117 Budapest, Hungary
- Email: zoli@renyi.hu
- Received by editor(s): March 28, 2007
- Received by editor(s) in revised form: June 17, 2007
- Published electronically: April 2, 2008
- Additional Notes: This research was supported by OTKA grant no. 61600.
- Communicated by: Alexander N. Dranishnikov
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 2979-2984
- MSC (2000): Primary 54A25, 54C10, 54D70
- DOI: https://doi.org/10.1090/S0002-9939-08-09315-5
- MathSciNet review: 2399066