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Keywords:
bend set; pairwise smooth continuum; contractible continuum; curve; dendroid; fan; homotopy; pointwise smooth continuum; $Q$-point; selectible continuum; absolute end point; arc-like; decomposition; irreducible; locally connected; smoth
bend set; pairwise smooth continuum; contractible continuum; curve; dendroid; fan; homotopy; pointwise smooth continuum; $Q$-point; selectible continuum; absolute end point; arc-like; decomposition; irreducible; locally connected; smoth
Summary:
A concept of an absolute end point introduced and studied by Ira Rosenholtz for arc-like continua is extended in the paper to be applied arbitrary irreducible continua. Some interrelations are studied between end points, absolute end points and points at which a given irreducible continuum is smooth.
References:
[1] R. H. Bing: Concerning hereditarily indecomposable continua. Pacific J. Math 1 (1951), 43-51. DOI 10.2140/pjm.1951.1.43 | MR 0043451 | Zbl 0043.16803
[2] R. H. Bing: Snake-like continua. Duke Math. J. 18 (1951), 653-663. DOI 10.1215/S0012-7094-51-01857-1 | MR 0043450 | Zbl 0043.16804
[3] J. J. Charatonik: On irreducible smooth continua. Topology and its Applications II. Proc. International Symposium on Topology and its Applications, Budva 1972 (Beograd 1973), 45-50. MR 0345079
[4] J. J. Charatonik, T. Maćkowiak: Continua with a dense set of end points. Rocky Mountain J. Math. 17 (1987), 385-391. DOI 10.1216/RMJ-1987-17-2-385 | MR 0892465
[5] G. R. Gordh, Jr.: On decomposition of smooth continua. Fund. Math. 75(1972), 51-60. DOI 10.4064/fm-75-1-51-60 | MR 0317299
[6] G. R. Gordh, Jr.: Concerning closed quasi-orders on hereditarily unicoherent continua. Fund. Math. 78 (1973), 61-73. DOI 10.4064/fm-78-1-61-73 | MR 0322835 | Zbl 0253.54031
[7] K. Kuratowski: Topology, vol. II. Academic Press and PWN, 1968. DOI 10.1016/B978-0-12-429202-4.50011-X | MR 0259835
[8] T. Maćkowiak: On smooth continua. Fund. Math. 85 (1974), 79-95. DOI 10.4064/fm-85-1-79-95 | MR 0365532
[9] I. Rosenholtz: Absolute endpoints of chainable continua. Proc. Amer. Math. Soc. 108 (1988), 1305-1314. DOI 10.1090/S0002-9939-1988-0955027-2 | MR 0955027 | Zbl 0655.54024
[10] E. S. Thomas, Jr.: Monotone decomposition of irreducible continua. Dissertationes Math. (Rozprawy Mat.) 50 (1966), 1-74. MR 0196721
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