TY - JOUR
T1 - On topological Kadec norms
AU - Abry, M.
AU - Dijkstra, J.J.
N1 - MR2179775
PY - 2005
Y1 - 2005
N2 - We present a topological analogue of the classic Kadec Renorming Theorem, as follows. Let W ⊂ S be two separable metric topologies on the same set X. We prove that every point in X has an S-neighbourhood basis consisting of sets that are W-closed if and only if there exists a function φ: X→ ℝ that is W-lower semi-continuous and such that S is the weakest topology on X that contains W and that makes φ continuous. An immediate corollary is that the class of almost n-dimensional spaces consists precisely of the graphs of lower semi-continuous functions with at most n-dimensional domains. © Springer-Verlag 2005.
AB - We present a topological analogue of the classic Kadec Renorming Theorem, as follows. Let W ⊂ S be two separable metric topologies on the same set X. We prove that every point in X has an S-neighbourhood basis consisting of sets that are W-closed if and only if there exists a function φ: X→ ℝ that is W-lower semi-continuous and such that S is the weakest topology on X that contains W and that makes φ continuous. An immediate corollary is that the class of almost n-dimensional spaces consists precisely of the graphs of lower semi-continuous functions with at most n-dimensional domains. © Springer-Verlag 2005.
UR - https://www.scopus.com/pages/publications/22144473338
UR - https://www.scopus.com/inward/citedby.url?scp=22144473338&partnerID=8YFLogxK
U2 - 10.1007/s00208-005-0651-5
DO - 10.1007/s00208-005-0651-5
M3 - Article
SN - 0025-5831
VL - 332
SP - 759
EP - 765
JO - Mathematische Annalen
JF - Mathematische Annalen
IS - 4
ER -