Irreducibility of inverse limits on intervals

• Autorzy: David J. Ryden
• Języki publikacji: EN

Abstrakty

EN

A procedure for obtaining points of irreducibility for an inverse limit on intervals is developed. In connection with this, the following are included. A semiatriodic continuum is defined to be a continuum that contains no triod with interior. Characterizations of semiatriodic and unicoherent continua are given, as well as necessary and sufficient conditions for a subcontinuum of a semiatriodic and unicoherent continuum M to lie within the interior of a proper subcontinuum of M.

Słowa kluczowe

EN

continuum; irreducible; inverse limit; chainable; triod; unicoherent; indecomposable; absolutely terminal subcontinuum

Kategorie tematyczne

• 54F15: Continua and generalizations
• 54F99: None of the above, but in this section
• 54F65: Topological characterizations of particular spaces
• 54F55: Unicoherence, multicoherence

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2000
• Tom: 165
• Numer: 1
• Strony: 29-53

Daty

wydano

2000

otrzymano

1998-08-15

poprawiono

2000-04-25

Twórcy

autor

David J. Ryden

• Department of Mathematics and Statistics, University of Missouri-Rolla, Rolla, MO 65409-0020, U.S.A.

Bibliografia

• [1]D. E. Bennett and J. B. Fugate, Continua and their non-separating subcontinua, Dissertationes Math. 149 (1977).
• [2]R. H. Bing, Snake-like continua, Duke Math. J. 18 (1951), 653-663.
• [3]W. D. Collins, A property of atriodic continua, Illinois J. Math. 28 (1984), 480-486.
• [4]J. R. Isbell, Embeddings in inverse limits, Ann. of Math. 70 (1959), 73-84.
• [5]D. P. Kuykendall, Irreducibility in inverse limits of intervals, Master's Thesis, Univ. of Houston, 1969.
• [6]D. P. Kuykendall, Irreducibility and indecomposability in inverse limits, Fund. Math. 80 (1973), 265-270.
• [7]M. A. Owens, Extremal continua: a class of non-separating subcontinua, Topology Appl. 23 (1986), 263-270.
• [8]R. H. Sorgenfrey, Concerning triodic continua, Amer. J. Math. 66 (1944), 439-460.