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1998 | 75 | 2 | 195-203
Tytuł artykułu

Hereditarily weakly confluent induced mappings are homeomorphisms

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
For a given mapping f between continua we consider the induced mappings between the corresponding hyperspaces of closed subsets or of subcontinua. It is shown that if either of the two induced mappings is hereditarily weakly confluent (or hereditarily confluent, or hereditarily monotone, or atomic), then f is a homeomorphism, and consequently so are both the induced mappings. Similar results are obtained for mappings between cones over the domain and over the range continua.
Rocznik
Tom
75
Numer
2
Strony
195-203
Opis fizyczny
Daty
wydano
1998
otrzymano
1996-10-09
poprawiono
1997-04-25
Twórcy
  • Mathematical Institute, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
  • Mathematical Institute, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
Bibliografia
  • [1] R. D. Anderson, Atomic decompositions of continua, Duke Math. J. 24 (1956), 507-514.
  • [2] J. J. Charatonik and W. J. Charatonik, Lightness of induced mappings, Tsukuba J. Math., to appear.
  • [3] W. J. Charatonik, Arc approximation property and confluence of induced mappings, Rocky Mountain J. Math., to appear.
  • [4] A. Emeryk and Z. Horbanowicz, On atomic mappings, Colloq. Math. 27 (1973), 49-55.
  • [5] H. Hosokawa, Some remarks on the atomic mappings, Bull. Tokyo Gakugei Univ. (4) 40 (1988), 31-37.
  • [6] H. Hosokawa, Induced mappings between hyperspaces, ibid. 41 (1989), 1-6.
  • [7] H. Hosokawa, Induced mappings between hyperspaces II, ibid. 44 (1992), 1-7.
  • [8] H. Hosokawa, Induced mappings on hyperspaces, Tsukuba J. Math., to appear.
  • [9] H. Hosokawa, Induced mappings on hyperspaces II, ibid., to appear.
  • [10] A. Y. W. Lau, A note on monotone maps and hyperspaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 24 (1976), 121-123.
  • [11] T. Maćkowiak, Continuous mappings on continua, Dissertationes Math. (Rozprawy Mat.) 158 (1979).
  • [12] S. B. Nadler, Jr., Hyperspaces of Sets, Dekker, 1978.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv75z2p195bwm
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