Inheritance of local topological properties of schemes

This paper shows that for certain local topological properties, given a locally quasi-finite, flat and locally finitely presented map of schemes $f\text{\hspace{0.17em}⁣}:X\to Y$, if $Y$ has the property, then so does $X$. We also show that being locally topologically noetherian or locally connected or having locally finitely many irreducible components are examples for these local topological properties.