The surjective semispan for Hausdorff continua

It is well known that Tychonoff spaces are those whose topology is induced by a uniformity. We use this fact to give two characterizations of chainable continua; the first one in terms of V-chains and the other one in terms of V-maps. We also define the surjective semispan for Hausdorff continua and we prove that chainable continua has empty surjective semispan. As a consequence of this result we obtain that each map from a continuum onto a chainable continuum is universal; in particular, chainable continua have the fixed point property.