Ahmad Ja'Afari Kalvan

Finite-Point Metrizable Coarsenings: Compatible Gauges, Simplicial Metrics, and Hausdorff Lower Bounds

Let $(X,\tau)$ be metrizable and let $F=\{a_1,\ldots,a_k\}\subseteq X$, where $2\le k<\infty$. We represent all metrizable topologies $\sigma\subseteq\tau$ agreeing with $\tau$ on $X\setminus F$ by compatible systems of continuous gauges $s_i:X\to[0,1]$ with $s_i^{-1}(0)=\{a_i\}$. The condition $\inf_X\max\{s_i,s_j\}>0...