  Let $B$ be the one-point extension algebra of $A$ by an $A$-module $X$. We
proved that every support $\tau$-tilting $A$-module can be extended to be a
support $\tau$-tilting $B$-module by two different ways. As a consequence, it
is shown that there is an inequality $$|\stilt B|\geqslant 2|\stilt A|.$$

Representation Theory