A countable 𝑘-space that is not stratifiable

Foged, L.

doi:10.1090/S0002-9939-1981-0593485-X

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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A countable $k$-space that is not stratifiable
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by L. Foged PDF

Proc. Amer. Math. Soc. 81 (1981), 337-338 Request permission

Abstract:

We add a point to a countable metric space to obtain a regular Fréchet space which is not stratifiable.

References

Eric K. van Douwen and Roman Pol, Countable spaces without extension properties, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 25 (1977), no. 10, 987–991 (English, with Russian summary). MR 474182
Eric K. van Douwen, Nonstratifiable regular quotients of separable stratifiable spaces, Proc. Amer. Math. Soc. 52 (1975), 457–460. MR 375247, DOI 10.1090/S0002-9939-1975-0375247-9