On a Katuta-Junnila Problem

We consider the Katuta-Junnila problem. 1. Is a space metacompact if every directed open cover of the space has a cushioned refinement? 2. Is a space submetacompact if every directed open cover of the space has a σ-cushioned refinement? We summarize some previous known partial results and present an affirmative answer to problem 1 in the class of strongly first countable spaces. AMS subject classification: 54B10, 54D20.