Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

CATEGORICAL PROPERTIES OF SEMI-CONTINUOUS QUASI-ORDERED SPACES

  • Shin, Seon-Ho (Department of Mathematics, Sookmyung Womens University)
  • Published : 2002.10.01
Download PDF
⟨ Previous Next ⟩

Abstract

We study categorical properties of the category SWQOS (S$\^$U/WQOS, S$\^$L/WQOS, resp) of (upper, lower, resp.) semi-continuous quasi-ordered spaces and the subcategory SWPOS (S$\^$U/WPOS, S$\^$L/WPOS, resp.) of (upper, lower, resp.) semicontinuous partially ordered spaces. We show that the categories S$\^$U/WPOS, S$\^$L/WPOS and SWPOS are closed under the formation of initial mono-sources in the category TQOS of topological quasi-ordered spaces, and they we mono-topological, complete and cocomplete epireflective subcategories of the category TQOS. We obtain their MacNeille and universal initial completions, as well as those of subcatego.ies S$\^$U/WQOS(S$\^$L/WQOS) and SWQOS, in which the topologies are T$\_$0/ and T$_1$, respectively.

Keywords

References

  1. Abstract and Concrete Categories J. Adamek;H. Herrlich;G.E. Strecker
  2. Quaestiones Math v.8 Initial completions of monotopological categories and cartesian closeness I.W. Alderton
  3. General Topology N. Bourbaki
  4. An. Acad. brasil. Cienc v.51 no.1 Partially ordered topological spaces T.H. Choe
  5. Introductions to Lattices and Order B.A. Davey;H.A. Priestley
  6. Gen. Top. Appl v.4 Topological functors H. Herrlich https://doi.org/10.1016/0016-660X(74)90016-6
  7. Proc. Amer. Math. Soc. v.62 no.2 Cartesian closed topological hulls H. Herrich;L.D. Nel https://doi.org/10.2307/2041017
  8. Topology and Order L. Nachbin
  9. Math. Nachr v.163 On the MacNeille completion of the category of partially ordered topological spaces A. Schauerte https://doi.org/10.1002/mana.19931630123
  10. J. Nat. Sci. v.9 Order-separations for topological quasi-ordered spaces S.H. Shin
  11. Proc. Amer. Math. Soc. v.5 Partially ordered topological spaces L.E. Ward Jr. https://doi.org/10.2307/2032122