In non-archimedean analytic geometry, one considers:
Given a topological space, a quasinet in $X$ is a set $\tau = \{V_i\}$ of subsets of $X$ such that for each point $x\in X$ there exists a finite number of such subsets $V_{i_1}, \cdots, V_{i_n} \in \tau$ such that
$x\in V_{i_1} \cap V_{i_2} \cap \cdots \cap V_{i_n}$ (the point is in their intersection);
$V_{i_1} \cup \cdots \cup V_{i_n}$ is a neighbourhood of $x$.
(e.g. Berkovich 09, def. 3.1.1.)
A quasinet $\tau$ is called a net if for all $U,V \in \tau$ then the restriction $\tau|_{U \cap V}$ is a quasinet of $U \cap V$.
Created on July 17, 2014 at 22:12:06. See the history of this page for a list of all contributions to it.