Homeomorphism groups and the topologist's sine curve

• Autorzy: Dijkstra J. J. , Tahri R.
• Języki publikacji: EN

Abstrakty

EN

It is shown that deleting a point from the topologist's sine curve results in a locally compact connected space whose autohomeomorphism group is not a topological group when equipped with the compact-open topology.

Słowa kluczowe

EN

topologist's sine curve; homeomorphism group; topological group; compact-open topology

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2010
• Tom: Vol. 58, no 3
• Strony: 269--272
• Opis fizyczny: Bibliogr. 6 poz., wykr.

Twórcy

autor

Dijkstra J. J.

autor

Tahri R.

• Faculteit der Exacte Wetenschappen / Afdeling Wiskunde, Vrije Universiteit, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands,

Bibliografia

• [1] R. Arens, Topologies for homeomorphism groups, Amer. J. Math. 68 (1946), 593-610.
• [2] F. H. Groom, Principles of Topology, Saunders, Philadelphia, 1989.
• [3] J. J. Dijkstra, On homeomorphism groups and the compact-open topology, Amer. Math. Monthly 112 (2005), 910-912.
• [4] S. Mardešić and J. Segal, Shape Theory, North-Holland, Amsterdam, 1982.
• [5] J. R. Munkres, Topology, 2nd ed., Prentice Hall, Upper Saddle River, 2000.
• [6] L. A. Steen and J. A. Seebach, Counterexamples in Topology, Holt, Rinehart and Winston, New York, 1970.