Chinese Quarterly Journal of Mathematics ›› 2012, Vol. 27 ›› Issue (3): 447-451.

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On AP-property of Function Spaces 

  

  1. Department of Mathematics, Taizhou Teacher’s College; Department of Mathematics, Nanjing University

  • Received:2011-05-30 Online:2012-09-30 Published:2023-03-24
  • About author:SHEN Rong-xin(1981-), male, native of Taizhou, Jiangsu, an associate professor of Taizhou Teacher’s College, Ph.D., engages in general topology.
  • Supported by:
    Supported by the NNSF of China(10971185); Supported by the China Postdoctoral Science Foundation Funded Project(20090461093,201003571)； Supported by the Jiangsu Planned Projects for Postdoctoral Research Funds(0902064C)；Supported by the Taizhou Teachers’ College Research Funds

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Abstract:

In this paper, it is discussed the AP-property of function spaces. We prove that for any compact network α for a space X which is closed under finite unions, (1) if Cα(X) is an AP-space and X is paracompact, then X is a Hurewicz space; (2) if Cα(X) is an AP-space which has countable tightness, then Cα(X) is discretely generated.


Key words: AP-spaces, function spaces, Hurewics spaces, discretely generated spaces

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