Exposition
This page contains articles of my self-directed explorations in mathematics. Hopefully, you'd find them useful.

On Countability and Separability of Metrizable Spaces

June, 2025 | EN
This expository article discusses foundational topological properties of metrizable spaces related to bases countability and separability, which are some classical results in general and metric topology. While assuming the reader’s familiarity with basic topological concepts, the article briefly reviews foundational notions relevant to the proof, including topological bases, countability of bases, and separability. The proof is reconstructed with close attention to definitions and logical structure, aiming to serve as a learning document for students and enthusiasts of topology. No new results are claimed; the goal is to clarify a well-known implication in metric topology through self-guided exploration and careful exposition.

License: CC BY-NC-SA 4.0
Creative Commons License
CC BY-NC-SA 4.0

Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International

The works contained on this page are licensed under Attribution-NonCommercial-ShareAlike 4.0 International. To view a copy of this license, visit CC BY-NC-SA 4.0 or send a letter to Creative Commons, PO Box 1866, Mountain View, CA 94042, USA.

You are free to:

  • Share — copy and redistribute the material in any medium or format
  • Adapt — remix, transform, and build upon the material

The licensor cannot revoke these freedoms as long as you follow the license terms.

Under the following terms:

  • Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • NonCommercial — You may not use the material for commercial purposes.
  • ShareAlike — If you remix, transform, or build upon the material, you must distribute your contributions under the same license as the original.
  • No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.

Notices:

You do not have to comply with the license for elements of the material in the public domain or where your use is permitted by an applicable exception or limitation.

No warranties are given. The license may not give you all of the permissions necessary for your intended use. For example, other rights such as publicity, privacy, or moral rights may limit how you use the material.