A note on induced and coinduced fuzzy topologies (Q1112356)

If (X,\(\tau)\) is a topological space the authors call the topology w(\(\tau)\) of lower semi-continuous functions the `corresponding fuzzy topology'. The definition of `goodness' for a fuzzy topology is as follows: a property \(P_ f\) in (X,w(\(\tau)\)) is called a good extension of a property P in (X,\(\tau)\) when (X,w(\(\tau)\)) has \(P_ f\) iff (X,\(\tau)\) has P. The induced fuzzy topology and coinduced fuzzy topology, as defined usually, are `good'.