# The Stacks Project

## Tag 004L

• the open covering $\mathcal{V}$ is a refinement of the open covering $\mathcal{U}$ (if $\mathcal{V} : V = \bigcup_{j \in J} V_j$ and $\mathcal{U} : U = \bigcup_{i \in I} U_i$ this means each $V_j$ is completely contained in one of the $U_i$),
1. The code snippet corresponding to this tag is a part of the file topology.tex and is located in lines 81–88 (see updates for more information).

\item
\label{item-refinement}
the open covering $\mathcal{V}$ is a {\it refinement}
of the open covering $\mathcal{U}$ (if
$\mathcal{V} : V = \bigcup_{j \in J} V_j$ and
$\mathcal{U} : U = \bigcup_{i \in I} U_i$
this means each $V_j$ is completely contained in one of the $U_i$),

## Comments (1)

Comment #3234 by Fred Rohrer (site) on March 12, 2018 a 8:56 pm UTC

The refinement should cover the same set as the covering it refines, i.e., replace $V$ by $U$.

There are also 4 comments on Section 5.2: Topology.

There are also 4 comments on Section 5.2.

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