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Uspekhi Mat. Nauk, 1976, Volume 31, Issue 3(189), Pages 71–128 (Mi umn3722)  

This article is cited in 6 scientific papers (total in 6 papers)

Some questions of general topology and Tikhonov semifields. II

M. Ya. Antonovskii, D. V. Chudnovskii


Abstract: This article is, in the opinion of its authors, a natural continuation of the survey [4] (with a similar title). And if the main question in [4] was whether every ring homomorphism $\psi\colon R^\Delta\to R^{\Delta"}$ is continuous, so one of the main questions in this paper is whether every sequentially continuous map $f\colon R^\Delta\to R^{\Delta"}$ is continuous. This circle of questions is closely connected with works of Mazur, Keisler and Tarski, with [4], and with others, and leads us to consider new and very wide classes of cardinals. In particular, we consider the classes of sequential, strictly sequential, measurable, and compact cardinals.
We also clarify some of the connections between properties of the Tikhonov semifields $R^\Delta$ and the lattices $Z^\Delta$, $N^\Delta$ contained in them, with various questions of axiomatic and combinatorial set theory (see [18], [25], [75].)

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English version:
Russian Mathematical Surveys, 1976, 31:3, 69–128

Bibliographic databases:

UDC: 513.83
MSC: 54C05, 54A05, 54C10, 12J17, 54A25

Citation: M. Ya. Antonovskii, D. V. Chudnovskii, “Some questions of general topology and Tikhonov semifields. II”, Uspekhi Mat. Nauk, 31:3(189) (1976), 71–128; Russian Math. Surveys, 31:3 (1976), 69–128

Citation in format AMSBIB
\Bibitem{AntChu76}
\by M.~Ya.~Antonovskii, D.~V.~Chudnovskii
\paper Some questions of general topology and Tikhonov semifields.~II
\jour Uspekhi Mat. Nauk
\yr 1976
\vol 31
\issue 3(189)
\pages 71--128
\mathnet{http://mi.mathnet.ru/umn3722}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=450343}
\zmath{https://zbmath.org/?q=an:0355.54006}
\transl
\jour Russian Math. Surveys
\yr 1976
\vol 31
\issue 3
\pages 69--128
\crossref{https://doi.org/10.1070/RM1976v031n03ABEH001539}


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    This publication is cited in the following articles:
    1. R.H. Marty, “Sequential closure in product spaces”, Topology and its Applications, 14:3 (1982), 305  crossref
    2. V. I. Malykhin, “Topology and forcing”, Russian Math. Surveys, 38:1 (1983), 77–136  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. Grzegorz Plebanek, “On the space of continuous functions on a dyadic set”, Mathematika, 38:1 (1991), 42  crossref  mathscinet  zmath  isi
    4. Grzegorz Plebanek, “Compact spaces that result from adequate families of sets”, Topology and its Applications, 65:3 (1995), 257  crossref
    5. A.V. Arhangel'skiĩ, W. Just, “Dense, sequentially continuous maps on dyadic compacta”, Topology and its Applications, 64:1 (1995), 95  crossref
    6. Elói Medina Galego, “Spaces of compact operators on spaces”, Journal of Mathematical Analysis and Applications, 370:2 (2010), 406  crossref
  • Успехи математических наук Russian Mathematical Surveys
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