Between closed sets and generalized closed sets in closure spaces

Chawalit Boonpok; Jeeranunt Khampakdee

Acta Mathematica Universitatis Ostraviensis (2008)

  • Volume: 16, Issue: 1, page 3-14
  • ISSN: 1804-1388

Abstract

top
The purpose of the present paper is to define and study ∂ -closed sets in closure spaces obtained as generalization of the usual closed sets. We introduce the concepts of ∂ -continuous and ∂ -closed maps by using ∂ -closed sets and investigate some of their properties.

How to cite

top

Boonpok, Chawalit, and Khampakdee, Jeeranunt. "Between closed sets and generalized closed sets in closure spaces." Acta Mathematica Universitatis Ostraviensis 16.1 (2008): 3-14. <http://eudml.org/doc/35171>.

@article{Boonpok2008,
abstract = {The purpose of the present paper is to define and study $\partial $-closed sets in closure spaces obtained as generalization of the usual closed sets. We introduce the concepts of $\partial $-continuous and $\partial $-closed maps by using $\partial $-closed sets and investigate some of their properties.},
author = {Boonpok, Chawalit, Khampakdee, Jeeranunt},
journal = {Acta Mathematica Universitatis Ostraviensis},
keywords = {closure operator; generalized closed set; $\partial $-closed set; $\partial $-continuous map; closure operator; -closed set; -continuous map},
language = {eng},
number = {1},
pages = {3-14},
publisher = {University of Ostrava},
title = {Between closed sets and generalized closed sets in closure spaces},
url = {http://eudml.org/doc/35171},
volume = {16},
year = {2008},
}

TY - JOUR
AU - Boonpok, Chawalit
AU - Khampakdee, Jeeranunt
TI - Between closed sets and generalized closed sets in closure spaces
JO - Acta Mathematica Universitatis Ostraviensis
PY - 2008
PB - University of Ostrava
VL - 16
IS - 1
SP - 3
EP - 14
AB - The purpose of the present paper is to define and study $\partial $-closed sets in closure spaces obtained as generalization of the usual closed sets. We introduce the concepts of $\partial $-continuous and $\partial $-closed maps by using $\partial $-closed sets and investigate some of their properties.
LA - eng
KW - closure operator; generalized closed set; $\partial $-closed set; $\partial $-continuous map; closure operator; -closed set; -continuous map
UR - http://eudml.org/doc/35171
ER -

References

top
  1. Arokiarani I., Balachandran K., Dontchev J., Some characterizations of gp-irresolute and gp-continuous maps between topological spaces, , Mem. Fac. Sci. Kochi Univ. Ser. A Math., 20 (1999), 93–104. (1999) Zbl0923.54015MR1684940
  2. Balachandran K., Sundaram P., Maki H., On generalized continuous maps maps in topological spaces, , Mem. Fac. Sci. Kochi Univ. Ser. A Math., 12 (1991), 5–13. (1991) MR1093540
  3. Boonpok C., Generalized closed sets in closure spaces, , to appear. Zbl1194.54004
  4. Čech E., Topological Spaces, , Topological Papers of Eduard Čech, Academia, Prague 1968, 436–472. (1968) 
  5. Chvalina J., On homeomorphic topologies and equivalent set-systems, , Arch. Math. 2, Scripta Fac. Sci. Nat. UJEP Brunensis, XII (1976), 107–116. (1976) Zbl0349.54002MR0438267
  6. Chvalina J., Stackbases in power sets of neighbourhood spaces preserving the continuity of mappings, , Arch. Math. 2, Scripta Fac. Sci. Nat. UJEP Brunensis, XVII (1981), 81–86. (1981) Zbl0478.54001MR0673249
  7. Cueva M.C., On g-closed sets and g-continuous mapping, , Kyungpook Math. J., 33(1993), 205–209. (1993) MR1253672
  8. Gnanabal Y., On generalized preregular closed sets in topological spaces, , Indian J. Pure & Appl. Math., 28 (3) (1977), 351–360. (1977) MR1442845
  9. Levine N., 10.2307/2312781, , Amer. Math. Monthly, 70 (1963), 36–41. (1963) Zbl0113.16304MR0166752DOI10.2307/2312781
  10. Levine N., 10.1007/BF02843888, , Rend. Circ. Mat. Palermo, 19 (1970), 89–96. (1970) Zbl0231.54001MR0305341DOI10.1007/BF02843888
  11. Maki H., Devi R., Balachandran K., Generalized α -closed sets in topology, , Bull. Fukuoka Univ. Ed. Part III, 42 (1993), 13–21. (1993) Zbl0888.54005
  12. Njastad O., 10.2140/pjm.1965.15.961, , Pacific J. Math. 15 (1965), 961–970. (1965) Zbl0137.41903MR0195040DOI10.2140/pjm.1965.15.961
  13. Palaniappan N., Rao K.C., Regular generalized closed sets, , Kyungpook Math. J., 33(1993), 211–219. (1993) Zbl0794.54002MR1253673
  14. Skula L., Systeme von stetigen abbildungen, Czech. Math. J, , 17 (92) (1967), 45–52. (1967) MR0206917
  15. Šlapal J., 10.1016/S0304-3975(02)00708-9, , Theoret. Comput. Sci., 305 (2003), 457–471. MR2013581DOI10.1016/S0304-3975(02)00708-9

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.