Quotient fuzzy topological spaces (Q5947620)

The author proves that a continuous function \(f\) which maps a topological space \((X,\tau)\) to another topological space \((Y,\eta)\) is a quotient map if and only if \(f:(X,\omega(\tau))\to (Y,\omega (\eta))\) is a quotient map, where \(\omega\) denotes the Lowen functor from the category of topological spaces to that of fuzzy topological spaces. This conclusion is a trivial corollary of the well-known fact that the Lowen functor embeds the category of topological spaces in that of stratified fuzzy topological spaces as a simultaneously bireflective and bicoreflective full subcategory.