THE IDEMPOTENT RELATION AND THE PROOF OF URYSOHN'S LEMMA

  • Kim, Seungwook (Department of Mathematics Hankuk University of Foreign Studies)
  • Received : 2008.09.22
  • Published : 2009.12.30

Abstract

The Urysohn's lemma which is crucial tool for the study of the metrization problem is proved in the sense of set-theoretic concept, namely, by the idempotent relation defined on a given topology.

Keywords

References

  1. Franz W., Topology I, Walter de Gruyter (1973).
  2. Querenburg B. V., Mengentheoretische Topologie, Springer Verlag (2001).
  3. Schubert H., Topology, Teubner (1975).
  4. Steen L. A. Seebach, JR. J. A., Counterexamples in topology, Springer Verlag (1995).