Abstract
A topological spaceX is called weakly first countable, if for every pointx there is a countable family {C xn |n ∈ω} such thatx ∈C +1xn ⊆C xn and such thatU ⊂X is open iff for eachx ∈U someC xn is contained inU. This weakening of first countability is due to A. V. Arhangelskii from 1966, who asked whether compact weakly first countable spaces are first countable. In 1976, N. N. Jakovlev gave a negative answer under the assumption of continuum hypothesis. His result was strengthened by V. I. Malykhin in 1982, again under CH. In the present paper we construct various Jakovlev type spaces under the weaker assumption b=c, and also by forcing.
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The second author was supported by the Ben-Gurion University Center for Advanced Studies in Mathematics, Be’er Sheva.
The third author was supported by OTKA grant no. 37758 of Hungary.
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Abraham, U., Gorelic, I. & Juhász, I. On Jakovlev spaces. Isr. J. Math. 152, 205–219 (2006). https://doi.org/10.1007/BF02771983
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DOI: https://doi.org/10.1007/BF02771983