Perhaps it is worth mentioning that this is not the only assign filter to a given net in a "reasonable" way. (Reasonable meaning that it preserves some properties, such as convergence, cluster points, etc.) There is also a correspondence which will preserve finer filter/subnets in both direction (unlike this one), although the definition of the net corresponding to a given filter becomes more complicated. You can read more about this in Pete L. Clark's notes on convergence. — Martin Sleziak 27 secs ago
Suppose $G$ is a finer filter than $F$ in a topological space $X$.
Is the net base in $G$ a subnet of the net base in $F$?
I am using the definitions of General Topology of Willard:
Definition 12.15. If $(x_\lambda)$ is a net in $X$, the filter generated by the filter base $\mathscr C$ cons...
