Continuous images of arcs

Nikiel, Jacek

doi:10.1090/S0002-9939-1988-0947691-9

Continuous images of arcs
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Proc. Amer. Math. Soc. 103 (1988), 961-968 Request permission

Abstract:

A characterization of continuous images of (Hausdorff) arcs is used to describe their cyclic elements as inverse limits of inverse systems of ’nice’ spaces with ’nice’ bonding mappings.

References

C. E. Capel, Inverse limit spaces, Duke Math. J. 21 (1954), 233–245. MR 62417
J. L. Cornette, “Image of a Hausdorff arc” is cyclically extensible and reducible, Trans. Amer. Math. Soc. 199 (1974), 253–267. MR 375257, DOI 10.1090/S0002-9947-1974-0375257-5
Ryszard Engelking, Topologia ogólna, Państwowe Wydawnictwo Naukowe, Warsaw, 1975 (Polish). Biblioteka Matematyczna, Tom 47. [Mathematics Library. Vol. 47]. MR 0500779
G. R. Gordh Jr. and Sibe Mardešić, Characterizing local connectedness in inverse limits, Pacific J. Math. 58 (1975), no. 2, 411–417. MR 385784

Mengentheoretische Charakterisierung der stetigen Kurven

123

John G. Hocking and Gail S. Young, Topology, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1961. MR 0125557
Sibe Mardešić, On the Hahn-Mazurkiewicz theorem in nonmetric spaces, Proc. Amer. Math. Soc. 11 (1960), 929–937. MR 117688, DOI 10.1090/S0002-9939-1960-0117688-X
Sibe Mardešić, Locally connected ordered and chainable continua, Rad Jugoslav. Akad. Znan. Umjet. Odjel Mat. Fiz. Tehn. Nauke 319 (1961), 147–166 (Serbo-Croatian, with English summary). MR 0148036

On the Hahn-Mazurkiewicz problem in non-metric spaces

Sur les lignes de Jordan

1

Jan van Mill and Evert Wattel, Dendrons, Topology and order structures, Part 1 (Lubbock, Tex., 1980) Math. Centre Tracts, vol. 142, Math. Centrum, Amsterdam, 1981, pp. 59–81. MR 630541
Jacek Nikiel, Images of arcs—a nonseparable version of the Hahn-Mazurkiewicz theorem, Fund. Math. 129 (1988), no. 2, 91–120. MR 959435, DOI 10.4064/fm-129-2-91-120

An elementary proof of a theorem of S. Mardešić

101

A continuous partial ordering for images of arcs

B. J. Pearson, Mapping arcs and dendritic spaces onto netlike continua, Colloq. Math. 34 (1975/76), no. 1, 39–48. MR 405373, DOI 10.4064/cm-34-1-39-48
L. B. Treybig, Arcwise connectivity in continuous images of ordered compacta, Glas. Mat. Ser. III 21(41) (1986), no. 1, 201–211 (English, with Serbo-Croatian summary). MR 866765
L. B. Treybig and L. E. Ward Jr., The Hahn-Mazurkiewicz problem, Topology and order structures, Part 1 (Lubbock, Tex., 1980) Math. Centre Tracts, vol. 142, Math. Centrum, Amsterdam, 1981, pp. 95–105. MR 630543
L. E. Ward Jr., The Hahn-Mazurkiewicz theorem for rim-finite continua, General Topology and Appl. 6 (1976), no. 2, 183–190. MR 402698
L. E. Ward Jr., A generalization of the Hahn-Mazurkiewicz theorem, Proc. Amer. Math. Soc. 58 (1976), 369–374. MR 413063, DOI 10.1090/S0002-9939-1976-0413063-0
Gordon Thomas Whyburn, Analytic Topology, American Mathematical Society Colloquium Publications, Vol. 28, American Mathematical Society, New York, 1942. MR 0007095
Gordon T. Whyburn, Cut points in general topological spaces, Proc. Nat. Acad. Sci. U.S.A. 61 (1968), 380–387. MR 242129, DOI 10.1073/pnas.61.2.380
G. S. Young, Representations of Banach spaces, Proc. Amer. Math. Soc. 13 (1962), 667–668. MR 143007, DOI 10.1090/S0002-9939-1962-0143007-0