Topological Groups and Covering Dimension
We consider a natural way of extending the Lebesgue covering dimension to various classes of infinite dimensional topological groups. The dimension function that we introduce extends Lebesgue covering dimension, has the hereditary property, and has a product theory that is more similar to the product theory for the finite dimensional case.
Babinkostova, Liljana. (2011). "Topological Groups and Covering Dimension". Topology and its Applications, 158(12), 1460-1470. http://dx.doi.org/10.1016/j.topol.2011.05.018