Jan 1, 0001
Point-to-point convergence
$f_n \rightarrow g \iff \forall x \in X \hookrightarrow f_n(x) \rightarrow g(x)$.
Topology
Pre-topology-base $V_{f, x, \varepsilon} = {g \in F: |f(x) - g(x)| < \varepsilon}$ builds a topology.
Jan 1, 0001
$f_n \rightarrow g \iff \forall x \in X \hookrightarrow f_n(x) \rightarrow g(x)$.
Pre-topology-base $V_{f, x, \varepsilon} = {g \in F: |f(x) - g(x)| < \varepsilon}$ builds a topology.