A Characterization of Chainable Continua
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 383-393
Voir la notice de l'article provenant de la source Cambridge University Press
In this paper, certain results of Bing (1) and myself (2) are extended. It is well-known that a chainable compact metric continuum must be a-triodic (contain no triods), hereditarily unicoherent (the common part of each two subcontinua is connected), and each subcontinuum must be chainable. Our principal result states that a compact metric continuum M is chainable if and only if M is a-triodic, hereditarily unicoherent and each indecomposable subcontinuum of M is chainable. Some condition on the indecomposable subcontinua of M seems essential, if we consider the dyadic solenoid, 5, which is indecomposable, a-triodic and hereditarily unicoherent. Indeed, each proper subcontinuum of S is an arc. However, S is not chainable, since it cannot be embedded in the plane.
Fugate, J. B. A Characterization of Chainable Continua. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 383-393. doi: 10.4153/CJM-1969-040-x
@article{10_4153_CJM_1969_040_x,
author = {Fugate, J. B.},
title = {A {Characterization} of {Chainable} {Continua}},
journal = {Canadian journal of mathematics},
pages = {383--393},
year = {1969},
volume = {21},
number = {1},
doi = {10.4153/CJM-1969-040-x},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1969-040-x/}
}
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