A note on connected and peripherally continuous functions

Author:
Melvin R. Hagan

Journal:
Proc. Amer. Math. Soc. **26** (1970), 219-223

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 monotone-light factorization theorem is proved for certain connected functions and peripherally continuous functions.

**[1]**Melvin R. Hagan,*Upper semi-continuous decompositions and factorization of certain non-continuous transformations*, Duke Math. J.**32**(1965), 679–687. MR**0187215****[2]**O. H. Hamilton,*Fixed points for certain noncontinuous transformations*, Proc. Amer. Math. Soc.**8**(1957), 750–756. MR**0087095**, 10.1090/S0002-9939-1957-0087095-7**[3]**Paul E. Long,*Properties of certain non-continuous transformations*, Duke Math. J.**28**(1961), 639–645. MR**0133111****[4]**Paul E. Long,*Connected mappings*, Duke Math. J.**35**(1968), 677–682. MR**0234428****[5]**R. L. Moore,*Foundations of point set theory*, Revised edition. American Mathematical Society Colloquium Publications, Vol. XIII, American Mathematical Society, Providence, R.I., 1962. MR**0150722****[6]**William J. Pervin and Norman Levine,*Connected mappings of Hausdorff spaces*, Proc. Amer. Math. Soc.**9**(1958), 488–496. MR**0095468**, 10.1090/S0002-9939-1958-0095468-2**[7]**Gordon Thomas Whyburn,*Analytic topology*, American Mathematical Society Colloquium Publications, Vol. XXVIII, American Mathematical Society, Providence, R.I., 1963. MR**0182943**

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DOI:
https://doi.org/10.1090/S0002-9939-1970-0263042-6

Keywords:
Open monotone connected function,
peripherally continuous function,
unicoherent continuum,
hereditarily locally connected continuum,
upper semicontinuous decomposition,
monotone-light factorization

Article copyright:
© Copyright 1970
American Mathematical Society