A note on locally pathwise connected metric spaces
In 1932, Whyburn construced a new metric \(d^{*}\) from a given metric \(d\) by changing all the distances \(d(x,y)\) into the distances \(d^{*}(x,y)\), where \(d^{*}(x,y)\) is the infimum of the numbers \(d(C)\) for any connected set \(C\) containing \(x,\;y\), \(d(C)\) being the distances of \(C\). The author studies an analogous construction for locally pathwise connected metric spaces and gives an application of this by showing that the category of uniformly locally pathwise connected metric spaces and uniformly continuous maps is coreflective in the category of metric spaces and uniformly continuous maps.
scientific article; zbMATH DE number 5324372