An approximation topology using countable elementary submodels

Authors

  • Makoto Kurosaki

Keywords:

elementary submodel, metrization theorem, $\Sigma$-product

Abstract

We introduce an approximation topology using countable elementary submodels and prove some classic theorems on generalized metric spaces.

References

Jurij H. Bregman, A note about M1-spaces and stratifiable spaces, Comment Math Univ Carol. 24 (1983), issue 1, 23-30.

J. Chaber, On point-countable collections and monotonic properties, Fund. Math. 94 (1977), 209-219.

A. Dow, An introduction to applications of elementary submodels to topology, Topology Proc. 13 (1988), 17-72.

G. Gruenhage, Stratifiable spaces are M2, Topology Proc. 1 (1976), 221-226.

G. Gruenhage, Generalized metric spaces, in : Handbook of Set-Theoretic Topology, North-Holland, Amsterdam (1984), 423-501.

Richard E. Hodel, Modern Metrization Theorems, in : Encyclopedia of General Topology, Elsevier Science Publishers B.V., (2004), 242-246.

H. J. K. Junnila, Neighbornets, Pacific J. Math. 76 (1978), 83-108.

A. Miščenko, Spaces with a point-countable base, Soviet Math. Dokl. 3, (1962), 855-858.

J. Nagata, A note on Filipov's Theorem, Proc. Japan Acad. 45, (1969), 30-33.

S. Oka, Dimension of stratifiable spaces, Trans. Amer. Math. Soc. 275 (1983), 231-243.

V. E. Šnider, Continuous images of Souslin and Borel sets; metrization theorems, Dokl. Acad. Nauk. USSR, 50, (1945), 77-79.

Y. Yajima, The normality of $\Sigma$-products and the perfect $\kappa$-normality of Cartesian products, J. Math. Soc. Japan 36 (1984), 689-699.

Y. Yajima, On $\Sigma$-products of semi-stratifiable spaces, Topology Appl. 25 (1987), 1-11.

Published

2025-07-18

How to Cite

Kurosaki, M. (2025). An approximation topology using countable elementary submodels. Topology Proceedings, 66, 165–176. Retrieved from https://topology.journals.yorku.ca/index.php/tp/article/view/172

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Section

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