A note on connected and peripherally continuous functions
Author:
Melvin R. Hagan
Journal:
Proc. Amer. Math. Soc. 26 (1970), 219223
MSC:
Primary 54.60
MathSciNet review:
0263042
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Abstract: In this paper it is proved that under certain conditions on the domain and range spaces an open monotone connected function preserves unicoherentness and hereditary local connectedness. In addition, a monotonelight factorization theorem is proved for certain connected functions and peripherally continuous functions.
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 [1]
 M. R. Hagan, Upper semicontinuous decompositions and factorization of certain noncontinuous transformations, Duke Math. J. 32 (1965), 679687. MR 32 #4668. MR 0187215 (32:4668)
 [2]
 O. H. Hamilton, Fixed points for certain noncontinuous transformations, Proc. Amer. Math. Soc. 8 (1957), 750756. MR 19, 301. MR 0087095 (19:301b)
 [3]
 P. E. Long, Properties of certain noncontinuous transformations, Duke Math. J. 28 (1961), 639645. MR 24 #A2945. MR 0133111 (24:A2945)
 [4]
 , Connected mappings, Duke Math. J. 35 (1968), 677682. MR 38 #2745. MR 0234428 (38:2745)
 [5]
 R. L. Moore, Foundations of point set theory, rev. ed., Amer. Math. Soc. Colloq. Publ., vol. 13, Amer. Math. Soc., Providence, R.I., 1962. MR 27 #709. MR 0150722 (27:709)
 [6]
 W. J. Pervin and Norman Levine, Connected mappings of Hausdorff spaces, Proc. Amer. Math. Soc. 9 (1958), 488496. MR 20 #1970. MR 0095468 (20:1970)
 [7]
 G. T. Whyburn, Analytic topology, Amer. Math. Soc. Colloq. Publ., vol. 28, Amer. Math. Soc., Providence, R.I., 1963. MR 32 #425. MR 0182943 (32:425)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939197002630426
PII:
S 00029939(1970)02630426
Keywords:
Open monotone connected function,
peripherally continuous function,
unicoherent continuum,
hereditarily locally connected continuum,
upper semicontinuous decomposition,
monotonelight factorization
Article copyright:
© Copyright 1970
American Mathematical Society
