[see also: set]
Instead of dealing with lines one by one, we deal with collections of lines simultaneously.
Neighbourhoods of points in these spaces appear at first glance to have a nice regular structure, but upon closer scrutiny, one sees that many neighbourhoods contain collections of arcs hopelessly folded up.
Continuing in this fashion, we get a collection $\{V_r\}$ of open sets, one for every rational $r$, with ......
Next we relabel the collection $\{A_n,B_n\}$ as $\{C_n\}$.
The words collection, family and class will be used synonymously with set.
The theorem implies that some finite subcollection of the $f_i$ can be removed without altering the span.
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