Glasnik Matematicki, Vol. 43, No.1 (2008), 219-229.

ČECH-COMPLETE MAPS

Yun-Feng Bai and Takuo Miwa

Department of Mathematics, Shimane University, Matsue 690-8504, Japan
(Capital Normal University, Beijin, China)
e-mail: yuntingbai@126.com

Department of Mathematics, Shimane University, Matsue 690-8504, Japan
e-mail: miwa@riko.shimane-u.ac.jp

Abstract.   We introduce a new notion of "Čech-complete map", and investigate some its basic properties, invariance under perfect maps, characterizations by compactifications of Čech-complete maps and relationships between (locally) compact map, Čech-complete map and k-map.

2000 Mathematics Subject Classification.   55R70, 54C10, 54D35.

Key words and phrases.   Fibrewise topology, Čech-complete map, compact map, k-map, compactification of map, T2-compactifiable map.

Full text (PDF) (free access)

DOI: 10.3336/gm.43.1.15

References:

  1. I. V. Bludova and G. Nordo, On the posets of all the Hausdorff and all the Tychonoff compactifications of mappings, Q & A in General Topology 17 (1999), 47-55.
    MathSciNet

  2. D. Buhagiar, Paracompact maps, Q & A in General Topology 15 (1997), 203-223.
    MathSciNet

  3. D. Buhagiar and T. Miwa, Covering properties on maps, Q & A in General Topology 16 (1998), 53-66.
    MathSciNet

  4. D. Buhagiar, T. Miwa and B.A. Pasynkov, On metrizable type (MT-)maps and spaces, Topology and its Appl. 96 (1999), 31-51.
    MathSciNet     CrossRef

  5. R. Engelking, General Topology, Heldermann, Berlin, rev. ed., 1989.
    MathSciNet

  6. I. M. James, Fibrewise Topology, Cambridge Univ. Press, Cambridge, 1989.
    MathSciNet

  7. G. Nordo and B. A. Pasynkov, Perfect compactifications, Comment. Math. Univ. Carolinae 41 (2000), 619-629.
    MathSciNet

  8. B. A. Pasynkov, On the extension to maps of certain notions and assertions concerning spaces, in: Maps and Functors, Moscow State Univ., Moscow, (1984), 72-102 (in Russian).

  9. B. A. Pasynkov, Elements of the general topology of continuous maps, in: D.K.Musaev and B.A.Pasynkov, On Compactness and Completeness Properties of Topological Spaces, Tashkent, "FAN" Acad. of Sci. Uzbekistan Rep., (1994), 50-120 (in Russian).

  10. I. A. Wainstein, On closed maps of metric spaces, Dokl. Acad. Sci. USSR 57 (1947), 319-321 (in Russian).

  11. G. T. Whyburn, Compactification of mappings, Math. Ann. 166 (1966), 168-174.
    MathSciNet     CrossRef
Glasnik Matematicki Home Page