In non-archimedean analytic geometry, one considers:

Given a topological space, a quasinet in XX is a set τ={V i}\tau = \{V_i\} of subsets of XX such that for each point xXx\in X there exists a finite number of such subsets V i 1,,V i nτV_{i_1}, \cdots, V_{i_n} \in \tau such that

  1. xV i 1V i 2V i nx\in V_{i_1} \cap V_{i_2} \cap \cdots \cap V_{i_n} (the point is in their intersection);

  2. V i 1V i nV_{i_1} \cup \cdots \cup V_{i_n} is a neighbourhood of xx.

(e.g. Berkovich 09, def. 3.1.1.)

A quasinet τ\tau is called a net if for all U,VτU,V \in \tau then the restriction τ| UV\tau|_{U \cap V} is a quasinet of UVU \cap V.



  • Vladimir Berkovich, Non-archimedean analytic spaces, lectures at the Advanced School on pp-adic Analysis and Applications, ICTP, Trieste, 31 August - 11 September 2009 (pdf)

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