ArticleOriginal scientific text
Title
Four mapping problems of Maćkowiak
Authors 1, 2
Affiliations
- Department of Mathematics, Arizona State University, Tempe, Arizona 85287-1804, U.S.A.
- Department of Mathematics and Statistics, California State Iniversity, Chico, Chico, California 95929-0525, U.S.A.
Abstract
In his paper "Continuous mappings on continua" [5], T. Maćkowiak collected results concerning mappings on metric continua. These results are theorems, counterexamples, and unsolved problems and are listed in a series of tables at the ends of chapters. It is the purpose of the present paper to provide solutions (three proofs and one example) to four of those problems.
Keywords
local dendrite, (weak) limit property, hereditarily divisible by points, weakly confluent map, (hereditarily) n-confluent map, atriodic map, composition factor property, locally monotone map, (hereditarily) partially confluent map
Bibliography
- R. H. Bing and F. B. Jones, Another homogeneous plane continuum, Trans. Amer. Math. Soc. 90 (1959), 171-192.
- J. Dugundji, Topology, Allyn and Bacon, Boston, 1966.
- F. B. Jones, On a certain type of homogeneous plane continuum, Proc. Amer. Math. Soc. 6 (1955), 735-740.
- K. Kuratowski, Topology, Vol. II, Academic Press, New York, 1968.
- T. Maćkowiak, Continuous mappings on continua, Dissertationes Math. (Rozprawy Mat.) 158 (1979).
- V. C. Nall, Maps which preserve graphs, Proc. Amer. Math. Soc. 101 (1987), 563-570.
- V. C. Nall, Partially confluent maps and n-ods, Houston J. Math. 15 (1989), 409-415.
Pages:
133-141
Main language of publication
English
Received
1994-10-03
Published
1996
Exact and natural sciences