On topological groups of automorphisms

Buzyakova, Raushan ^[1]
1. [1] Polk State College
  
  Polk State College
  
  Estados Unidos
Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 26, Nº. 2, 2025, págs. 633-640
Idioma: inglés
DOI: 10.4995/agt.2025.21941
Enlaces
- Texto completo
Resumen
- We study spaces X for which the space Homp(X) of automorphisms with the topology of point-wise convergence is a topological group. We identify large classes of spaces X for which Homp(X) is or is not a topological group.
Referencias bibliográficas
- A. Arhangelskii and M. Tkachenko, Topological Groups and Related Structures, Atlantis Press/World Scientific, 2008. https://doi.org/10.2991/978-94-91216-35-0
- R. Buzyakova, On topological groups of automorphisms on unions, Rocky Mountain Journal of Mathematics, accepted.
- R. Engelking, General Topology, PWN, Warszawa, 1977.
- J. Dijkstra and J. Van Mill, On the group of homeomorphisms of the real line that map pseudoboundary onto itself, Canad. J. Math. Vol. 58,...
- M. Gheysens, The homeomorphism group of the first uncountable ordinal, Enseign. Math. 67), no. 1/2 (2021), 145-159. https://doi.org/10.4171/lem/1006
- B. V. Sorin, Compactifications of homeomorphism groups of linearly ordered compacta, Mathematical Notes 112 (2022), 126-141. https://doi.org/10.1134/S0001434622070148
- G. S. Ungar, Countable dense homogeneity and n-homogeneity, Fund. Math. 99, no. 3 (1978), 155–160. https://doi.org/10.4064/fm-99-3-155-160