A characterization of spaces on which all path maps are continuous
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 .
-  Eric Bedford, Path maps and continuity, Proc. Amer. Math. Soc. 24 (1970), 112–115. MR 0253302, https://doi.org/10.1090/S0002-9939-1970-0253302-7
-  James Dugundji, Topology, Allyn and Bacon, Inc., Boston, Mass., 1966. MR 0193606
-  S. P. Franklin, Spaces in which sequences suffice, Fund. Math. 57 (1965), 107–115. MR 0180954, https://doi.org/10.4064/fm-57-1-107-115
-  P. W. Harley III, On sequential spaces and maps (submitted).
- E. Bedford, Path maps and continuity, Proc. Amer. Math. Soc. 24 (1970), 112-115. MR 40 #6517. MR 0253302 (40:6517)
- J. Dugundgi, Topology, Allyn and Bacon, Boston, Mass., 1966. MR 33 #1824. MR 0193606 (33:1824)
- S. P. Franklin, Spaces in which sequences suffice, Fund. Math. 57 (1965), 107-115. MR 31 #5184. MR 0180954 (31:5184)
- 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