The Stacks project

6.2 Basic notions

The following is a list of basic notions in topology.

1. Let $X$ be a topological space. The phrase: “Let $U = \bigcup _{i \in I} U_ i$ be an open covering” means the following: $I$ is a set and for each $i \in I$ we are given an open subset $U_ i \subset X$ such that $U$ is the union of the $U_ i$. It is allowed to have $I = \emptyset$ in which case there are no $U_ i$ and $U = \emptyset$. It is also allowed, in case $I \not= \emptyset$ to have any or all of the $U_ i$ be empty.

2. etc, etc.