The projective -character bounds the order of a -base

Authors:
István Juhász and Zoltán Szentmiklóssy

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

Published electronically:
April 2, 2008

MathSciNet review:
2399066

Full-text PDF

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Abstract: All spaces below are Tychonov. We define the projective - character of a space as the supremum of the values where ranges over all (Tychonov) continuous images of . Our main result says that every space has a -base whose order is ; that is, every point in is contained in at most -many members of the -base. Since for compact , this is a significant generalization of a celebrated result of Shapirovskii.

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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

DOI:
https://doi.org/10.1090/S0002-9939-08-09315-5

Keywords:
Projective $\pi $-character,
order of a $\pi $-base,
irreducible map

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

Article copyright:
© Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.