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ArticleOriginal scientific text

Title

Irreducibility of inverse limits on intervals

Authors 1

Affiliations

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

Abstract

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.

Keywords

ENG
continuum, irreducible, inverse limit, chainable, triod, unicoherent, indecomposable, absolutely terminal subcontinuum

Bibliography

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  3. [3]W. D. Collins, A property of atriodic continua, Illinois J. Math. 28 (1984), 480-486.
  4. [4]J. R. Isbell, Embeddings in inverse limits, Ann. of Math. 70 (1959), 73-84.
  5. [5]D. P. Kuykendall, Irreducibility in inverse limits of intervals, Master's Thesis, Univ. of Houston, 1969.
  6. [6]D. P. Kuykendall, Irreducibility and indecomposability in inverse limits, Fund. Math. 80 (1973), 265-270.
  7. [7]M. A. Owens, Extremal continua: a class of non-separating subcontinua, Topology Appl. 23 (1986), 263-270.
  8. [8]R. H. Sorgenfrey, Concerning triodic continua, Amer. J. Math. 66 (1944), 439-460.
Fundamenta Mathematicae
2000/165/1
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Pages:
29-53
Main language of publication
English
Received
1998-08-15
Accepted
2000-04-25
Published
2000
Exact and natural sciences