Acta mathematica scientia,Series A ›› 2013, Vol. 33 ›› Issue (3): 483-493.

• Articles • Previous Articles     Next Articles

Weak Bases and the Compact-Covering Images of Metric Spaces

 LIN Shou1,2, ZHANG Jing3   

  1. 1.Department of Mathematics and |Information Science, Zhangzhou Normal University, Zhangzhou 363000;
    2.Institute of Mathematics, Ningde Normal University, Ningde 352100;
    3.Institute of Mathematics, Nanjing Normal University, Nanjing 210046
  • Received:2011-10-13 Revised:2013-02-05 Online:2013-06-25 Published:2013-06-25
  • Supported by:

    国家自然科学基金(10971185, 11171162)和福建省自然科学基金(2009J01013)资助

Abstract:

In this paper some equivalent conditions of a space in which each compact subset is metrizable and has a countable weak base in the space are obtained by means of sn-networks, the spaces are characterized as images of metric spaces under 1-scc~(resp. scc) and quotient maps, and spaces in which each compact subset has a countable outer weak base are discussed, which generalized the classic result about compact-covering and open images of metric spaces by Michael and Nagami.

Key words: sn-networks, Weak bases, Outer sn-networks, Outer weak bases, Compact-covering maps, 1-sequence-covering maps, Quotient maps,  1-scc-maps, scc-maps

CLC Number: 

  • 54C10
Trendmd