Groups of homeomorphisms on $C(X)$ and pointwise limits

Year, pages: 2013, 143 - 166

This study looks at some subgroups of the group $\mathcal{H}(C(X))$ 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 $\mathcal{H}(C(X))$ generated by the algebraic and vertical homeomorphisms on $C(X)$ is dense in $\mathcal{H}(C(X))$ with the pointwise topology. Also, for $X$ equal to the unit interval, a subgroup of $\mathcal{H}(C(X))$ 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 $\mathcal{H}(C(X))$ can have.

Mccoy, R. 2013. Groups of homeomorphisms on $C(X)$ and pointwise limits. In Mathematica Slovaca, vol. 63, no.1, pp. 143-166. 0139-9918. DOI: https://doi.org/10.2478/s12175-012-0089-7

Mccoy, R. (2013). Groups of homeomorphisms on $C(X)$ and pointwise limits. Mathematica Slovaca, 63(1), 143-166. 0139-9918. DOI: https://doi.org/10.2478/s12175-012-0089-7