The concept of  somewhat pairwise fuzzy $alpha$-irresolute continuous mappings and somewhat pairwise fuzzy irresolute $alpha$-open mappings have been introduced and studied. Besides, some interesting properties of those mappings are given.

We prove that discrete compact quantum groups (or more generally locally compact, under additional hypotheses) with coamenable dual are continuous fields over their central closed subgroups, and the same holds for free products of amalgamated a common subgroup. Along way we also show [Formula: see text]-algebras again via Fell-topology characterization text]-field continuity, recovering result ...

This article is an expository overview of the proof of the author that tightness of a closed contact 3-manifold is preserved under Legendrian surgery. The aim is to give a somewhat more leisurely, motivated, and illustrated version of the ideas and constructions involved in the original paper.