  In the literature there are two ways of endowing an affine ind-variety with a
topology. One possibility is due to Shafarevich and the other to Kambayashi. In
this paper we specify a large class of affine ind-varieties where these two
topologies differ. We give an example of an affine ind-variety that is
reducible with respect to Shafarevich's topology, but irreducible with respect
to Kambayashi's topology. Moreover, we give a counter-example of a supposed
irreducibility criterion of Shafarevich which is different from a
counter-example given by Homma. We finish the paper with an irreducibility
criterion similar to the one given by Shafarevich.
