# Irreducibility of inverse limits on intervals

Fundamenta Mathematicae (2000)

- Volume: 165, Issue: 1, page 29-53
- ISSN: 0016-2736

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topRyden, David. "Irreducibility of inverse limits on intervals." Fundamenta Mathematicae 165.1 (2000): 29-53. <http://eudml.org/doc/212459>.

@article{Ryden2000,

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.},

author = {Ryden, David},

journal = {Fundamenta Mathematicae},

keywords = {continuum; irreducible; inverse limit; chainable; triod; unicoherent; indecomposable; absolutely terminal subcontinuum; irreducible continuum; irreducibility; unicoherent continua},

language = {eng},

number = {1},

pages = {29-53},

title = {Irreducibility of inverse limits on intervals},

url = {http://eudml.org/doc/212459},

volume = {165},

year = {2000},

}

TY - JOUR

AU - Ryden, David

TI - Irreducibility of inverse limits on intervals

JO - Fundamenta Mathematicae

PY - 2000

VL - 165

IS - 1

SP - 29

EP - 53

AB - 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.

LA - eng

KW - continuum; irreducible; inverse limit; chainable; triod; unicoherent; indecomposable; absolutely terminal subcontinuum; irreducible continuum; irreducibility; unicoherent continua

UR - http://eudml.org/doc/212459

ER -

## References

top- [1]D. E. Bennett and J. B. Fugate, Continua and their non-separating subcontinua, Dissertationes Math. 149 (1977). Zbl0354.54017
- [2]R. H. Bing, Snake-like continua, Duke Math. J. 18 (1951), 653-663. Zbl0043.16804
- [3]W. D. Collins, A property of atriodic continua, Illinois J. Math. 28 (1984), 480-486. Zbl0524.54026
- [4]J. R. Isbell, Embeddings in inverse limits, Ann. of Math. 70 (1959), 73-84. Zbl0094.35405
- [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. Zbl0285.54026
- [7]M. A. Owens, Extremal continua: a class of non-separating subcontinua, Topology Appl. 23 (1986), 263-270. Zbl0598.54016
- [8]R. H. Sorgenfrey, Concerning triodic continua, Amer. J. Math. 66 (1944), 439-460. Zbl0060.40208

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