Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Example of a $ T\sb 1$ topological space without a Noetherian base


Authors: Angel Tamariz-Mascarúa and Richard G. Wilson
Journal: Proc. Amer. Math. Soc. 104 (1988), 310-312
MSC: Primary 54G20; Secondary 54D20
MathSciNet review: 958089
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] E. K. van Douwen, Noetherian bases (manuscript).
  • [2] I. Juhasz, Cardinal functions in topology, Mathematical Centre, Amsterdam, 1971.
  • [3] A. Tamariz-Mascarúa, Bases Noetherianas en espacios topológicos, Tesis Doctoral, Universidad Autónoma Metropolitana-Iztapalapa, 1986.
  • [4] -, Noetherian bases in ordinal spaces, Bol. Soc. Mat. Mexicana 30 (1985).

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54G20, 54D20

Retrieve articles in all journals with MSC: 54G20, 54D20


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0958089-1
PII: S 0002-9939(1988)0958089-1
Keywords: Noetherian base, $ N$-refinable space
Article copyright: © Copyright 1988 American Mathematical Society