Electronic Resource
Springer
Annali di matematica pura ed applicata
86 (1970), S. 25-29
ISSN:
1618-1891
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary The Aleksandrov-Urysohn conjecture about the cardinality of a first countable compact spare X is here given an equivalent formulation in terms of a generalized Lindelöf condition in the weak topology on X generated by the Baire functions. A number of related conditions are shown to be equivalent (without assuming that X is first countable); these include two sequential properties of the pointwise topology on various spaces of real-valued functions on X, and the condition that X is dispersed (i.e., has no non-void perfect subsets). Added in prof: The Alexandrov-Urysohn conjecture has been generalized and proved by A. V. Archangel' skii (On the cardinality of bicompacta satisfying the first axiom of countability, Dokl. Akad. Nauk SSSR 187 (1969) (Russian); translated as Soviet Math. Dokl. 10 (1969) pp. 951–955). In his more general theorem the compactness hypothesis is weakened to Lindelöf.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02415705
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