Maha Mohammed SAEED, Lutfi KALANTAN, Hala ALZUMI

C-Paracompactness and $C_2$-paracompactness

A topological space X is called C -paracompact if there exist a paracompact space Y and a bijective function f : X −→ Y such that the restriction f |A : A −→ f (A) is a homeomorphism for each compact subspace A ⊆ X . A topological space X is called C2 -paracompact if there exist a Hausdorff paracompact space Y and a bijective function f : X −→ Y such that the restriction f |A : A −→ f (A) is a homeomorphism for each compact subspace A ⊆ X . We investigate these two properties and produce some examples to illustrate the relationship between them and C -normality, minimal Hausdorff, and other properties.

PDF

___

[1] Al-Montasherey K. New results about the Alexandroff duplicate space. MSc, King Abdulaziz University, Jeddah, Saudi Arabia, 2015.
[2] AlZahrani S, Kalantan L. Epinormality. J Nonlinear Sci Appl 2016; 9: 5398-5402.
[3] AlZahrani S, Kalantan L. C-normal topological property. Filomat 2017; 31: 407-411.
[4] Berri MP. Minimal topological spaces. T Am Math Soc 1963; 108: 97-105.
[5] Bourbaki N. Topologie general. Actualites Sci Ind nos Hermann Paris 1951; 858-1142 (in French).
[6] Engelking R. On the double circumference of Alexandroff. Bull Acad Pol Sci Ser Astron Math Phys 1968; 16; 8: 629-634.
[7] Engelking R. General Topology. Warsaw, Poland: PWN, 1977.
[8] Gruenhage G. Generalized metric spaces. In: Kunen K, editor. Handbook of Set-Theoretic Topology. Amsterdam, the Netherlands: North-Holland, 1984, pp. 423-510.
[9] Kalantan L. Results about -normality. Topol Appl 2002; 125: 47-62.
[10] Kalantan L, Alhomieyed M. CC-normal topological spaces. Turk J Math 2017; 41: 749-755.
[11] Kalantan L, Szeptycki P. -normality and products of ordinals. Topol Appl 2002; 123: 537-545.
[12] Mrówka S. On completely regular spaces. Fund Math 1954; 41: 105-106.
[13] Parhomenko AS. On condensations into compact spaces. Izv Akad Nauk SSSR Ser Mat 1941; 5: 225-232.
[14] Porter JR, Stephenson RM. Minimal Hausdorff spaces - Then and now. In: Aull CE, Lowen R, editors. Handbook of the History of General Topology. Dordrecht, the Netherlands: Kluwer Academic Publishers, 1998, pp. 669-687.
[15] Shchepin EV. Real valued functions and spaces close to normal. Sib J Math 1972; 13: 1182-1196.
[16] Singal M, Singal AR. Mildly normal spaces. Kyungpook Math J 1973; 13: 29-31.
[17] Steen L, Seebach JA. Counterexamples in Topology. Mineola, NY, USA: USA; Dover Publications, 1995.
[18] van Douwen EK. The integers and topology. In: Kunen K, editor. Handbook of Set-Theoretic Topology. Amsterdam, the Netherlands: North-Holland, 1984, pp. 111-167.

ISSN: 1300-0098
Yayın Aralığı: Yılda 6 Sayı
Yayıncı: TÜBİTAK

Arşiv