Example of a $T_ 1$ topological space without a Noetherian base
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- by Angel Tamariz-MascarĂșa and Richard G. Wilson PDF
- Proc. Amer. Math. Soc. 104 (1988), 310-312 Request permission
Abstract:
A Noetherian base $\mathcal {B}$ of a topological space $X$ is a base for the topology of $X$ which has the following property: If ${B_1} \subset {B_2} \subset \cdots$ is a nondecreasing sequence of elements of $\mathcal {B}$, then ${\left \{ {{B_n}} \right \}_{n \in {\mathbf {N}}}}$ is finite. In this article we give an example of a ${T_1}$ topological space without a Noetherian base.References
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E. K. van Douwen, Noetherian bases (manuscript).
I. Juhasz, Cardinal functions in topology, Mathematical Centre, Amsterdam, 1971.
A. Tamariz-MascarĂșa, Bases Noetherianas en espacios topolĂłgicos, Tesis Doctoral, Universidad AutĂłnoma Metropolitana-Iztapalapa, 1986.
â, Noetherian bases in ordinal spaces, Bol. Soc. Mat. Mexicana 30 (1985).
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 104 (1988), 310-312
- MSC: Primary 54G20; Secondary 54D20
- DOI: https://doi.org/10.1090/S0002-9939-1988-0958089-1
- MathSciNet review: 958089