As in our previous paper [5], by the covering dimension of a topological space X, dim X notation, we mean the least integer n such that every finite normal open cover of X is refined by a fimite normal open cover of X ...
@rperezmarco Such an X should have dimension n (since dim(X\times R)\le dim X+1 by a Theorem of Morita https://t.co/4xQa2BH9j2
It seems hard to imagine that a dimension n space could be embedded uncountably many times in R^n, but that is conceivable.