Countable connected spaces
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- by Gary Glenn Miller
- Proc. Amer. Math. Soc. 26 (1970), 355-360
- DOI: https://doi.org/10.1090/S0002-9939-1970-0263005-0
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Abstract:
Two pathological countable topological spaces are constructed. Each is quasimetrizable and has a simple explicit quasimetric. One is a locally connected Hausdorff space and is an extension of the rationals. The other is a connected space which becomes totally disconnected upon the removal of a single point. This space satisfies the Urysohn separation property—a property between ${T_2}$ and ${T_3}$—and is an extension of the space of rational points in the plane. Both are one dimensional in the Menger-Urysohn [inductive] sense and infinite dimensional in the Lebesgue [covering] sense.References
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Bibliographic Information
- © Copyright 1970 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 26 (1970), 355-360
- MSC: Primary 54.20
- DOI: https://doi.org/10.1090/S0002-9939-1970-0263005-0
- MathSciNet review: 0263005