In this paper we give new sufficient and necessary conditions:for a Ba
nach space to be equivalently renormed with the Mazur intersection pro
perty, As a consequence, several examples and applications of these re
sults are obtained. Among them. it is proved that every Banach space e
mbeds isometrically into a Banach space with the Mazur intersection pr
operty, answering a question asked by Giles, Gregory, and Sims. We als
o prove that for every tree T, the space C-0(T) admits a norm with the
Mazur intersection property, solving a problem posed by Deville, Gode
froy, and Zizler. Finally, assuming the continuum hypothesis, we find
an example of an Asplund space admitting neither an equivalent norm wi
th the above property nor a nicely smooth norm. (C) 1997 Academic Pres
s.