# Weaker form of irreducible surjections

An irreducible surjection is usually defined as a continuous closed surjective map $f:X\rightarrow Y$ such that if for some closed set $C\subset X$ one has $f(C)=Y$ then $C=X$. In my dissertation I used a weaker form of this definition, removing the requirement of these functions being closed. I then defined them as quasi-irreducible surjections. Are there any applications of quasi-irreducible surjection elsewhere?

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