TY - JOUR
AU - Sioen, M.
AU - Verwulgen, S.
PY - 2003/10/01
Y2 - 2024/04/21
TI - Locally convex approach spaces
JF - Applied General Topology
JA - Appl. Gen. Topol.
VL - 4
IS - 2
SE -
DO - 10.4995/agt.2003.2031
UR - https://ojs.upv.es/index.php/AGT/article/view/2031
SP - 263-279
AB - <p>We continue the investigation of suitable structures for quantified functional analysis, by looking at the notion of local convexity in the setting of approach vector spaces as introduced in [6]. We prove that the locally convex objects are exactly the ones generated (in the usual approach sense) by collections of seminorms. Furthermore, we construct a quantified version of the projective tensor product and show that the locally convex objects admitting a decent exponential law with respect to it are precisely the seminormed spaces.</p>
ER -