## Abstract

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.

Original language | English |
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Pages (from-to) | 759-765 |

Journal | Mathematische Annalen |

Volume | 332 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2005 |