Continua in which all connected subsets are arcwise connected

Tymchatyn, E. D.

doi:10.1090/S0002-9947-1975-0365523-2

Continua in which all connected subsets are arcwise connected
HTML articles powered by AMS MathViewer

by E. D. Tymchatyn PDF

Trans. Amer. Math. Soc. 205 (1975), 317-331 Request permission

Abstract:

Let $X$ be a metric continuum such that every connected subset of $X$ is arcwise connected. Some facts concerning the distribution of local cutpoints of $X$ are obtained. These results are used to prove that $X$ is a regular curve.

References

B. Knaster and C. Kuratowski, A connected and connected im kleinen point set which contains no perfect subset, Bull. Amer. Math. Soc. 33 (1927), no. 1, 106–109. MR 1561328, DOI 10.1090/S0002-9904-1927-04326-9
E. D. Tymchatyn, Continua whose connected subsets are arcwise connected, Colloq. Math. 24 (1971/72), 169–174, 286. MR 310848, DOI 10.4064/cm-24-2-169-174
Gordon T. Whyburn, On the Existence of Totally Imperfect and Punctiform Connected Subsets in a Given Continuum, Amer. J. Math. 55 (1933), no. 1-4, 146–152. MR 1506952, DOI 10.2307/2371118
G. T. Whyburn, Local separating points of continua, Monatsh. Math. Phys. 36 (1929), no. 1, 305–314. MR 1549688, DOI 10.1007/BF02307620
G. T. Whyburn, Decompositions of Continua by Means of Local Separating Points, Amer. J. Math. 55 (1933), no. 1-4, 437–457. MR 1506978, DOI 10.2307/2371144
G. T. Whyburn, Sets of local separating points of a continuum, Bull. Amer. Math. Soc. 39 (1933), no. 2, 97–100. MR 1562558, DOI 10.1090/S0002-9904-1933-05567-2
G. T. Whyburn, Concerning points of continuous curves defined by certain im kleinen properties, Math. Ann. 102 (1930), no. 1, 313–336. MR 1512580, DOI 10.1007/BF01782349

Analytic topology

4

L. E. Ward Jr., Partially ordered topological spaces, Proc. Amer. Math. Soc. 5 (1954), 144–161. MR 63016, DOI 10.1090/S0002-9939-1954-0063016-5
L. Mohler, Cuts and weak cuts in metric continua, Proceedings of the University of Houston Point Set Topology Conference (Houston, Tex., 1971) Univ. Houston, Houston, Tex., 1971, pp. 5–8. MR 0410694