The projective  -character bounds the order of a  -base |
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| Authors: | Istvá n Juhá sz Zoltá n Szentmikló ssy |
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| Institution: | Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, POB 127, Budapest, H-1364 Hungary ; Department of Analysis, Eötvös Loránt University, Pázmány Péter sétány 1/A, 1117 Budapest, Hungary |
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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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| Keywords: | Projective $\pi $-character order of a $\pi $-base irreducible map |
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