# Locally connected fan

The *locally connected fan*, written $F_{\omega}$, is the union of countably many straight line segments of length tending to $0$, emanating from a point $p$ and disjoint away from $p$. We can think of $F_{\omega}$ as the dendrite with only one ramification point whose order is $\omega$.

# Properties

**Theorem:** Each open image of $F_{\omega}$ is homeomorphic to $F_{\omega}$.

**Proof:** █