Countability, Separability and Embedding

Avishek Adhikari () and Mahima Ranjan Adhikari ()
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Avishek Adhikari: Presidency University, Department of Mathematics
Mahima Ranjan Adhikari: Institute for Mathematics, Bioinformatics, Information Technology and Computer Science (IMBIC)

Chapter Chapter 7 in Basic Topology 1, 2022, pp 447-477 from Springer

Abstract: Abstract This chapter continues the study of special classes of topological spaces such as spaces satisfying either of the two axioms of countability formulated by Hausdorff in 1914 or satisfying the axiom of separability introduced by Frechét in 1906, both initiated in Chap. 3, which do not arise from the study of calculus and analysis in a natural way. They arise through a deep study of topology. The axiom of first countability arose through the study of convergent sequences.

Date: 2022
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DOI: 10.1007/978-981-16-6509-7_7

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