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A characterization of spaces on which all path maps are continuous

Author: P. W. Harley
Journal: Proc. Amer. Math. Soc. 34 (1972), 621-622
MSC: Primary 54C10
MathSciNet review: 0309050
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Abstract: Here it is shown that all path maps on a topological space X are continuous if and only if X is a quotient image of a locally path connected metric space. This characterization strengthens results of E. Bedford [1].

References [Enhancements On Off] (What's this?)

  • [1] E. Bedford, Path maps and continuity, Proc. Amer. Math. Soc. 24 (1970), 112-115. MR 40 #6517. MR 0253302 (40:6517)
  • [2] J. Dugundgi, Topology, Allyn and Bacon, Boston, Mass., 1966. MR 33 #1824. MR 0193606 (33:1824)
  • [3] S. P. Franklin, Spaces in which sequences suffice, Fund. Math. 57 (1965), 107-115. MR 31 #5184. MR 0180954 (31:5184)
  • [4] P. W. Harley III, On sequential spaces and maps (submitted).

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Keywords: Locally path connected, path maps, metric space, quotient maps
Article copyright: © Copyright 1972 American Mathematical Society

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