A note on topologies related to \((x^{\alpha})\)-porosity (Q2276786)

On base of the notion of \((x^{\alpha})\)-porosity and \((x^{\alpha})\)- strong porosity of a set in a metric space the author considers topologies \(T_{\alpha}\) and \(\tau_{\alpha}\) and proves that they are regular. Moreover, he says that \(T_{\alpha}\) \((\tau_{\alpha})\) is the coarsest topology for which all \(T^*_{\alpha}\) \((\tau^*_{\alpha})\) continuous real functions are continuous.