Locally compact space

In topology, a **locally compact space** is a topological space that, at each point, resembles compact spaces in some way. More formally, a topological space \( X \) is said to be locally compact if every point in \( X \) has a neighborhood that is compact. Here's a breakdown of the concept: 1. **Neighborhood**: A neighborhood of a point \( x \in X \) is any open set that contains \( x \).