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Countability, Separability and Embedding

In: Basic Topology 1

Author

Listed:
  • Avishek Adhikari

    (Presidency University, Department of Mathematics)

  • Mahima Ranjan Adhikari

    (Institute for Mathematics, Bioinformatics, Information Technology and Computer Science (IMBIC))

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.

Suggested Citation

  • Avishek Adhikari & Mahima Ranjan Adhikari, 2022. "Countability, Separability and Embedding," Springer Books, in: Basic Topology 1, chapter 0, pages 447-477, Springer.
    • Handle: RePEc:spr:sprchp:978-981-16-6509-7_7
    DOI: 10.1007/978-981-16-6509-7_7
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