@article{Sioen_Verwulgen_2003, title={Locally convex approach spaces}, volume={4}, url={https://polipapers.upv.es/index.php/AGT/article/view/2031}, DOI={10.4995/agt.2003.2031}, abstractNote={<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>}, number={2}, journal={Applied General Topology}, author={Sioen, M. and Verwulgen, S.}, year={2003}, month={Oct.}, pages={263–279} }