Geodesic
Simple Links in Locally Compact Connected Hausdorff Spaces are Nondegenerate
Canadian journal of mathematics, Tome 34 (1982) no. 2, pp. 349-355

Voir la notice de l'article provenant de la source Cambridge University Press

The fact that simple links in locally compact connected metric spaces are nondegenerate was probably first established by C. Kuratowski and G. T. Whyburn in [2], where it is proved for Peano continua. J. L. Kelley in [3] established it for arbitrary metric continua, and A. D. Wallace extended the theorem to Hausdorff continua in [4]. In [1], B. Lehman proved this theorem for locally compact, locally connected Hausdorff spaces. We will show that the locally connected property is not necessary.A continuum is a compact connected Hausdorff space. For any two points a and b of a connected space M, E(a, b) denotes the set of all points of M which separate a from b in M. The interval ab of M is the set E(a, b) ∪ {a, b}. 
John, David. Simple Links in Locally Compact Connected Hausdorff Spaces are Nondegenerate. Canadian journal of mathematics, Tome 34 (1982) no. 2, pp. 349-355. doi: 10.4153/CJM-1982-022-2
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[1] 1. Lehman, B., Cyclic element theory in connected and locally connected Hausdorff spaces, Can. J. Math. 27 (1976), 1032–1050. Google Scholar

[2] 2. Kuratowski, C. et Whyburn, G. T., Sur les éléments cycliques et leurs applications, Fundamenta Mathematicae 16 (1930), 305–331. Google Scholar

[3] 3. Kelley, J. L., A decomposition of compact continua and related theorems on fixed sets under continuous transformations, Proceedings of the National Academy of Sciences 26 (1940), 192–194. Google Scholar

[4] 4. Wallace, A. D., Monotone transformations, Duke Mathematical Journal 9 (1942), 487–506. Google Scholar

[5] 5. Ward, L. E., Jr., A general fixed point theorem, Colloquium Mathematicum 15 (1966), 243–251. Google Scholar

[6] 6. Whyburn, G. T., Analytic topology First Edition, American Mathematical Society Colloquium Publications 28 (American Mathematical Society, Providence, RI, 1942). Google Scholar

[7] 7. Whyburn, G. T., Semi locally connected sets, American Journal of Mathematics 61 (1939), 733–749. Google Scholar

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