THE MAZUR INTERSECTION PROPERTY AND ASPLUND SPACES

We answer a question posed by J. R. Giles, D. A. Gregory and B. Sims, on the Mazur intersection property, by exhibiting a class of non Asplu nd spaces admitting an equivalent norm with the above property. On the other hand, if the continuum hypothesis is assumed, we find an Asplun d space admitting no equivalent norm with the Mazur intersection prope rty and whose dual space admits no equivalent norm with the weak Maz ur intersection property.