Year: 2013
Type: article
Abstract: This study looks at some subgroups of the group H(C(X)) of homeomorphisms on the space C(X) of continuous real-valued functions on a topological space X, where C(X) has the compact-open topology. The main result shows that, for certain spaces X, the subgroup of H(C(X)) generated by the algebraic and vertical homeomorphisms on C(X) is dense in H(C(X)) with the pointwise topology. Also, for X equal to the unit interval, a subgroup of H(C(X)) is developed using integration of the members of C(X), and this subgroup is used as an example and to illustrate certain properties that subgroups of H(C(X)) can have.
Source: Mathematica Slovaca
Author: R. McCoy
Institution: Virginia Tech
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,712
OpenAlex ID: W2060984618