ArticleOriginal scientific text

Title

Semi-open sets in biclosure spaces

Authors 1, 1

Affiliations

  1. Department of Mathematics, Brno University of Technology, Technická 2, 616 69 Brno, Czech Republic

Abstract

The aim of this paper is to introduce and study semi-open sets in biclosure spaces. We define semi-continuous maps and semi-irresolute maps and investigate their behavior. Moreover, we introduce pre-semi-open maps in biclosure spaces and study some of their properties.

Keywords

closure operator, biclosure space, semi-open set, semi-continuous map, semi-irresolute map, pre semi-open map

Bibliography

  1. J.M. Aarts and M. Mršević, A bitopological view on cocompact extensions, Topol. Appl. 83 (1991), 1-16.
  2. C. Boonpok and J. Khampakdee, Generalized closed sets in biclosure spaces, to appear.
  3. E. Čech, Topological spaces, (revised by Z. Frolík, M. Katětov), Academia, Prague 1966.
  4. E. Čech, Topological spaces, Topological papers of Eduard Čech, Academia, Prague (1968), 436-472.
  5. J. Chvalina, On homeomorphic topologies and equivalent set-systems, Arch. Math. Scripta Fac. Sci. Nat. UJEP Brunensis, XII 2 (1976), 107-116.
  6. J. Chvalina, Stackbases in power sets of neighbourhood spaces preserving the continuity of mappings, Arch. Math., Scripta Fac. Sci. Nat. UJEP Brunensis, XVII 2 (1981), 81-86.
  7. J. Deak, On bitopological spaces, I, Stud. Sci. Math. Hungar. 25 (1990), 457-481.
  8. B. Dvalishvili, On some bitopological applications, Mat.Vesn. 42 (1990), 155-165.
  9. J. Khampakdee, Semi-open sets in closure spaces, to appear.
  10. J.C. Kelly, Bitopological spaces, Proc. London Math. Soc. 3 (13) (1969), 71-79.
  11. N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly 70 (1963), 36-41.
  12. J. Šlapal, Closure operations for digital topology, Theoret. Comput. Sci. 305 (2003), 457-471.
Pages:
181-201
Main language of publication
English
Received
2009-04-29
Accepted
2009-07-01
Published
2009
Exact and natural sciences