Locally Connected
Description: A space $X$ is said to be locally connected if at each $x \in X$ and every neighborhood $U$ of $x$, there is a connected neighborhood $V$ of $x$ contained in $U$.
Description: A space $X$ is said to be locally connected if at each $x \in X$ and every neighborhood $U$ of $x$, there is a connected neighborhood $V$ of $x$ contained in $U$.