Is $\{\{a\}\}$ always a basis for the system of neighborhoods at $a$? If yes, what is the significance of the basis?
I am reading the definition in Mendelson's "Introduction to Topology" book at DEFINITION 4.9:
"Let $a$ be a point in a metric space $X$. A collection $\mathscr{B}_a$ of neighborhoods of $a$ is called a basis for the neighborhood system at $a$ if every neighborhood $N$ of $a$ contains some element $B$ of $\mathscr{B}_a$."