Particular point topology

Particular point topology is a type of topological space characterized by the presence of a designated "particular point" in the space. More formally, let \( X \) be a set, and let \( p \) be a specific element of \( X \). We define a topology \( \tau \) on \( X \) by specifying the open sets in the following way: 1. The empty set \( \emptyset \) is an open set.