Locally Compact Path Spaces

被引:0
作者
S. B. Niefield
机构
[1] Union College,
来源
Applied Categorical Structures | 2005年 / 13卷
关键词
locally compact; compact-open topology; path space;
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学科分类号
摘要
It is shown that the space X[0,1], of continuous maps [0,1]→X with the compact-open topology, is not locally compact for any space X having a nonconstant path of closed points. For a T1-space X, it follows that X[0,1] is locally compact if and only if X is locally compact and totally path-disconnected.
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页码:65 / 69
页数:4
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  • [1] Day B. J.(1970)On topological quotients preserved by pullback or products Proc. Cambridge Philos. Soc. 67 553-558
  • [2] Kelly G. M.(1945)On topologies for function spaces Bull. Amer. Math. Soc. 51 429-432
  • [3] Fox R. H.(1978)The spectral theory of distributive continuous lattices Trans. Amer. Math. Soc. 246 285-310
  • [4] Hofmann K. H.(1995)All compact Hausdorff lambda models are degenerate Fund. Inform. 122 23-52
  • [5] Lawson J. D.(1986)General function spaces, products, and continuous lattices Proc. Cambridge Philos. Soc. 100 193-205
  • [6] Hofmann K. H.(1968)Bi-quotient maps and cartesian products of quotient maps Ann. Inst. Fourier (Grenoble) 18 287-302
  • [7] Mislove M. W.(1982)Cartesianness: Topological spaces, uniform spaces, and affine schemes J. Pure Appl. Algebra 23 147-167
  • [8] Isbell J. R.(2002)Exponentiability of perfect maps: Four approaches Theory Appl. Categ. 10 127-133
  • [9] Michael E.(undefined)undefined undefined undefined undefined-undefined
  • [10] Niefield S. B.(undefined)undefined undefined undefined undefined-undefined