Trond A. Abrahamsen, Olav Nygaard and Märt Põldvere
Vol. 301 (2019), No. 2, 385–394
DOI: 10.2140/pjm.2019.301.385
Abstract
Let
be an infinite
locally compact Hausdorff topological space. We show that extremely regular subspaces of
have very strong
diameter
properties and,
for every real number
with
, contain
an
-isometric
copy of
.
If
does not contain isolated points they even have the Daugavet
property, and thus contain an asymptotically isometric copy of
.
Keywords
extremely regular function space, strong diameter 2
property, almost square space, octahedrality, Daugavet
property