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Nov 10, 2017 at 10:03 comment added Ramiro de la Vega Yes @DominicvanderZypen , this has the same flavor as a star-finite covering but quite stronger. Note that if $\varphi$ takes the constant value $X$ then it produces the star-finite covering $\{X\}$ but $\varphi$ does not have property 2 (unless $X$ is finite!).
Nov 10, 2017 at 5:58 comment added Dominic van der Zypen Very nice property! It's a bit like star-finite covering, no? (Possibly I mix up something...)
Nov 9, 2017 at 16:29 history asked Ramiro de la Vega CC BY-SA 3.0