Pointwise directed families of maps

Happy New Year 2017!  Sorry I have not posted for some time…  Today, let me talk about a curious construction of Lawson and Xi on families of continuous maps that are not directed, rather pointwise directed.  They use that to show that the dcpo of all Scott-continuous maps from a core-compact, core-coherent space to an RB-domain is a continuous dcpo; but the idea of pointwise directed families of maps, and the way they use it to find a basis of dcpos of continuous maps, is intriguing.  Read the full post.