Have a personal or library account? Click to login
Finite Dimensional Real Normed Spaces are Proper Metric Spaces Cover

Finite Dimensional Real Normed Spaces are Proper Metric Spaces

Open Access
|Jul 2022

References

  1. [1] Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pąk, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261–279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007/978-3-319-20615-8_17.
  2. [2] Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, and Karol Pąk. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9–32, 2018. doi:10.1007/s10817-017-9440-6.604425130069070
  3. [3] Noboru Endou and Yasunari Shidama. Completeness of the real Euclidean space. Formalized Mathematics, 13(4):577–580, 2005.
  4. [4] Hiroshi Imura, Morishige Kimura, and Yasunari Shidama. The differentiable functions on normed linear spaces. Formalized Mathematics, 12(3):321–327, 2004.
  5. [5] Miyadera Isao. Functional Analysis. Riko-Gaku-Sya, 1972.
  6. [6] Robert Milewski. Associated matrix of linear map. Formalized Mathematics, 5(3):339–345, 1996.
  7. [7] Laurent Schwartz. Théorie des ensembles et topologie, tome 1. Analyse. Hermann, 1997.
  8. [8] Yasunari Shidama. Differentiable functions on normed linear spaces. Formalized Mathematics, 20(1):31–40, 2012. doi:10.2478/v10037-012-0005-1.
  9. [9] Kôsaku Yosida. Functional Analysis. Springer, 1980.
DOI: https://doi.org/10.2478/forma-2021-0017 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630
Language: English
Page range: 175 - 184
Accepted on: Sep 30, 2021
|
Published on: Jul 9, 2022
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year

© 2022 Kazuhisa Nakasho, Hiroyuki Okazaki, Yasunari Shidama, published by University of Białystok
This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 License.