Refinable maps and 𝜃_{𝑛}-continua

Grace, E. E.; Vought, Eldon J.

doi:10.1090/S0002-9939-1989-0964455-1

Refinable maps and $\theta _ n$-continua
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by E. E. Grace and Eldon J. Vought PDF

Proc. Amer. Math. Soc. 106 (1989), 231-239 Request permission

Abstract:

Many properties of continua, e.g., irreducibility, span zero, and various kinds of aposyndesis and unicoherence, are preserved by refinable maps or their inverses. The purpose of this paper is to consider the extent to which the property of being a ${\theta ’_n}$-continuum is preserved by refinable maps or by inverses of refinable maps. One consequence of this study is to generalize results of the first author where the domain or range is a graph. Several of his results are corollaries of ours.

References

R. W. FitzGerald, Connected sets with a finite disconnection property, Studies in topology (Proc. Conf., Univ. North Carolina, Charlotte, N.C., 1974; dedicated to Math. Sect. Polish Acad. Sci.), Academic Press, New York, 1975, pp. 139–173. MR 0365478
Jo Ford and J. W. Rogers Jr., Refinable maps, Colloq. Math. 39 (1978), no. 2, 263–269. MR 522365, DOI 10.4064/cm-39-2-263-269
E. E. Grace, Refinable maps on graphs are near homeomorphisms, Topology Proc. 2 (1977), no. 1, 139–149 (1978). MR 540601
E. E. Grace and Eldon J. Vought, Monotone decompositions of $\theta _{n}$-continua, Trans. Amer. Math. Soc. 263 (1981), no. 1, 261–270. MR 590423, DOI 10.1090/S0002-9947-1981-0590423-5

Quasi-monotone mappings on

-continua

17

Hiroshi Hosokawa, Aposyndesis and coherence of continua under refinable maps, Tsukuba J. Math. 7 (1983), no. 2, 367–372. MR 723864, DOI 10.21099/tkbjm/1496159832
F. Burton Jones, Concerning non-aposyndetic continua, Amer. J. Math. 70 (1948), 403–413. MR 25161, DOI 10.2307/2372339