DOI: https://doi.org/10.14710/jfma.v6i2.18504

TOPOLOGY OF QUASI-PSEUDOMETRIC SPACES AND CONTINUOUS LINEAR OPERATOR ON ASYMMETRIC NORMED SPACES

*Klatenia Selawati  -  Departemen Matematika, Universitas Gadjah Mada, Sekip Utara Bulaksumur Yogyakarta 55281., Indonesia
Christiana Rini Indrati  -  Departemen Matematika, Universitas Gadjah Mada, Sekip Utara, Bulaksumur, Yogyakarta, Indonesia 55281., Indonesia

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Abstract
In this paper, we will discuss about topological properties of quasi-pseudometric spaces and properties of linear operators in asymmetric normed spaces. The topological properties of quasi-pseudometric spaces will be given consisting of open and closed set properties in quasi-pseudometric spaces. The discussion about properties of linear operators on asymmetric normed spaces is focused on the uniform boundedness principle. The uniform boundedness theorem is proved by utilizing completeness properties and characteristic of closed sets on quasi-pseudometric spaces.
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Section: FUNDAMENTAL MATHEMATICS AND APPLICATIONS
Language : ID
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  1. R. J. Duffin, and L. A. Karlovitz, L. ”Formulation of linear programs in analysis Approximation theory,” SIAM Journal on Applied Mathematics., vol. 16, no.4, pp. 662-675, 1968
  2. S. Cobzas, ”Compact Bilinear Operators on Asymmetric Normed Spaces,” Topology and its Applications, no. 306, article id. 107922, 2022
  3. L. M. Garcia-Raffi, S. Somaguera, and E. A. Sanchez-Perez, ”The Dual Spaces of an Asymmetric Normed Linear Space,” Questiones Mathematicae, vol.26, no.1, pp. 83-96, 2003
  4. S. K. Berberian, Introduction to Hilbert Space. New York: Oxford University Press, 1961
  5. S. Cobzas, Functional Analysis in Asymmetric Normed Space. New York: Springer Verlaq, 2013
  6. K. Keimel and W. Roth, Ordered Cones and Approximation. New York: Springer-Verlaq, 1992
  7. J. C. Kelly, ”Bitopological Spaces,” London Math, no.12, pp. 71-89, 1962
  8. E. Kreyszing. Introductory Functional Amalysis with Applications. New York: John Willey and Sons, 1978
  9. M. D. Mabula and S. Cobzas, ”Zambrejko’s Lemma and the Fundametal Principles of Functional Analysis in the Asymmetric Case,” Topology and its Applications, no. 184, pp. 1-15, 2015
  10. I. L. Reilly, P. V. Subrahmayan, and M. K. Vamanamurthy, ”Cauchy Sequences in Quasi Pseudo-Metric Spaces,” Monatshefte fur Mathematik by Springer-Verlag, no.93, pp. 127-140, 1982
  11. S. Romaguera, ”Left K-Completeness in Quasi-Metric Spaces,” Math Nachr, no. 157, pp. 15-23, 1992
  12. O. Valero, ”Quotient Normed Cones,” Proc. Indian Acad. Sci. (Math. Sci), vol. 116, no.2, pp. 175-191, 2006
  13. W. A. Wilson, ”On quasi-metric spaces,” American Journal of Mathematics, vol. 53, no.3, pp. 675-684, 1931
  14. J. Weidman. Linear Operations in Hilbert Spaces. New York: Springer Verlag, 1980

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