Definition
A first-countable space is a Topological Space whose Topology has a countable Local Basis.
Facts
Every Metric Space is a first-countable space.
The Product Space of two first-countable spaces is a first-countable space.
A first-countable space is a Topological Space whose Topology has a countable Local Basis.
Every Metric Space is a first-countable space.
The Product Space of two first-countable spaces is a first-countable space.