InOn representation spaces, a forthcoming article,José G. Anaya, Félix Capulín, Włodzimierz J. Charatonik, andFernando Orozco-Zitli have introduced the representation spaceCof all continua (up to homeomorphism). Here, we reproduce theargument that it is a topological space, and then we investigate itsconnectedness properties. Specifically, we show thatChas exactlytwo components, and we demonstrate that the subspaceN, consist-ing of all nondegenerate continua, is itself connected and even pathconnected. Moreover, we show that there exists a single continuumLsuch thatNis the closure of the class of{L}.