a group, such as the set of all real numbers, that constitutes a topological space and in which multiplication and inversion are continuous
topological group in American English
noun
Math
a set that is a group and a topological space and for which the group operation andthe map of an element to its inverse are continuous functions
Word origin
[1945–50]This word is first recorded in the period 1945–50. Other words that entered Englishat around the same time include: RNA, individual medley, regression analysis, shootout, taxi squad
Examples of 'topological group' in a sentence
topological group
Some properties of the compactification lattice of a topological group are obtained.
Wei He, Zhiqiang Xiao 2019, 'Lattice of compactifications of a topological group', Categories and General Algebraic Structures with Applicationshttp://www.cgasa.ir/article_61406_5c0d76f764a8ff7460747ef9016d1a97.pdf. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Generalizing some of the techniques yield decompositions for elements in a topological group.
Thomas P. Dence 1980, 'A Lebesgue decomposition for elements in a topological group', International Journal of Mathematics and Mathematical Scienceshttp://dx.doi.org/10.1155/S0161171280000609. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
In this paper, we studied the subgroup in β-α-topological group and several basic theorems are introduced.
Hariwan Z. Ibrahim, Alias B. Khalaf 2018, 'Normal Subgroups and Quotient Groups in β-α-topological Group', General Letters in Mathematicshttp://www.refaad.com/Files/GLM/GLM-5-1-3.pdf. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)