On fuzzy subspaces
The authors suggest fuzzy topological subspaces of a fuzzy topological space as structures induced over each fuzzy subset from the fuzzy topology; they define the concept of fuzzy topological subspace as follows: ``Let \((X,\delta)\) be a fuzzy topological space and \(\mu \in I^ X\), then the family \(\delta_ \mu = \{\nu\wedge\mu:\nu\in\delta\}\) is the fuzzy \(\mu\)-topology induced over \(\mu\) by \(\delta\). The elements of \(\delta_ \mu\) are called fuzzy \(\mu\)-open sets''. The authors introduce the concepts of \(\mu\)-closed sets, the \(\mu\)- neighbourhood of a fuzzy point, the \(\mu\)-basis of \(\delta_ \mu\), the \(\mu\)-local base at a point, fuzzy \(\mu\)-continuity, \(\mu\)-interior, \(\mu\)-closure, the \(\mu\)-isolated point and they investigate some usual topological properties. The authors finally introduce the concepts of \(\mu\)-prefilter, fuzzy \(\mu\)-ultrafilter, \(\mu\)-convergence and fuzzy compactness and characterize some fuzzy topological concepts via \(\mu\)- convergence.
scientific article; zbMATH DE number 516660