대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제36권4호
  • /
  • Pages.717-722
  • /
  • 1999
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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ON THE DUALITY OF THE SPACE X AND THE ALGEBRA $C_p$(X)

  • Park, Sung-Ki (Department of Mathematics Education , Chosun University)
  • 발행 : 1999.11.01
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초록

The set of continuous maps of a space X to real usual space R equipped with the toplogy of pointwise convergence will be denoted by $C_p$(X). In this paper, we prove that; $C_p$(X) is hereditarily separable and hereditary Lindelof if and only if $X^n$ is hereditarily separable and hereditary Lindelof.

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참고문헌

  1. Russian Math. Surveys v.38 no.5 Function spaces in the topology of pointwise convergence and compact set Arkhangel'skii A. V.
  2. Osaka Math. v.2 no.2 On lattices of functions on topological spaces and of functions on uniform space Nagata, J.
  3. Proc. Am. Math. Soc. v.1 The density character of function spaces Noble, N.
  4. Moscow Univ. Math. bull. v.40 no.4 The spaces of functions in the topology of pointwise convergence Okunev, O. G.
  5. Topol. Apple. The spaces$C_p(X)$decomposition into a countable union of bounded subspaces and completeness properties Tkacuk, V. V.