Abstract
In Sect. 5.2, we have seen that the notions of countable compactness and sequential compactness coincide for topological spaces which have countable local bases. A more important but restricted class of spaces consists of the ones which have countable bases. The first section concerns with such spaces. There are two other properties, namely, separability and Lindelöfness which are described by using the notion of countability, and each of them guarantees the existence of countable bases in metrizable spaces. These are treated in the second section.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2019 Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Singh, T.B. (2019). Countability Axioms. In: Introduction to Topology. Springer, Singapore. https://doi.org/10.1007/978-981-13-6954-4_7
Download citation
DOI: https://doi.org/10.1007/978-981-13-6954-4_7
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-13-6953-7
Online ISBN: 978-981-13-6954-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)