December 2019, Vol. 2, Issue 12, p. 71-74.​​

On the Baire’s Category Theorem as an Important Tool in General Topology and Functional Analysis
Amos Otieno Wanjara
Kaimosi Friends University College, School of Mathematics, Statistics, and Actuarial Science, P.O BOX 385-50309, Kaimosi-Kenya.
*Corresponding author’s e-mail:


The problems connected with Topological spaces, Metric spaces, Banach spaces, Boundedness and continuous mappings lie at the heart of Baire’s Category theorem. In this paper, we give a short survey on some classical results due to the Baire’s Category theorem in the field of general Topology and Functional analysis.

Keywords: Category; Interior of asset; empty interior; Baire space; open mapping; locally compact Hausdorff space; Metric space.


  1. Blair Ch E. The Baire category theorem, implies the principle of dependent choices. Bull Acad. Polon. Sciences 25 (1977) 933-4.
  2. James D, Topology, (Allyn and Bacon series in Advanced mathematics), Allyn and Bacon, Inc.Boston, 1966.
  3. Kelly JL, Namioka I. Linear topological spaces, Springer-Verlag, 1982.
  4. Kelly JL. General topology, Springer-Verlag, 1991.
  5. Levy A. Basic set theory. Reprinted by Dover, 2002.
  6. Leigh J. Functional analysis and linear control theory, Academic Press, New York. 1982.
  7. Munkress, James R. Topology, A first course, Prentice-Hall, 1975.
  8. Munkress JR. Topology (2nd ed).New York: Prentice Hall, 2008.
  9. Narici LE. Beckenstein, Bachman G. Functional analysis and valuation theory, Marcel Dekker, New York, 1971.
  10. Narici L, Beckenstein E. Topological vector spaces, Marcel Dekker, New York, 1985
  11. Rudin W. Functional analysis, Mc Graw-Hill, 1973.
  12. Rolewicz S.  Functional analysis and control theory, Reidel, Warsaw, 1987.
  13. Rudin W. Functional Analysis. New York: Mc Graw-Hill, 1991.
ISSN 2581-5954

International Journal of Modern Computation, Information and Communication Technology