On fuzzy pseudo-metric spaces
Results of the paper include the following: Result 1. Let \(d_1\) and \(d_2\) be fuzzy pseudo-metrics for \(X\) and \(Y\), respectively. If \(F:(X,d_1)\to (Y,d_2)\) is continuous, then \(F:(X,\text{Id}_1)\to (Y,\text{Id}_2)\) is continuous. Result 2. Let \(\phi\) be a pseudo-metric chain on \(X\). Let \(d_\phi\) be a fuzzy pseudo-matrix for \(X\). Then \(I_{d_\phi}= I_\phi\). Result 3. Let \(F:(X,d_1)\to (Y,d_2)\) be continuous. Then \(F: (X, U^{d_1})\to (Y,U^{d_2})\) is uniformly continuous, where \(U^{d_1}\) and \(U^{d_2}\) are fuzzifying uniformities on \(X\) and \(Y\), respectively.
scientific article; zbMATH DE number 5706285
scientific article