Metric space/Continuous function/Positive/Positive in neighborhood/Exercise

Let ${}(M,d)$ be a metric space, and let

$f\colon M\longrightarrow \mathbb {R}$

denote a continuous function. Let ${}x\in M$ be a point with ${}f(x)>0$. Show that also ${}f(y)>0$ holds for all ${}y$ from an open ball neighbourhood of ${}x$.

Create a solution