Moving forward, this repository will be the primary way of collaborating and contributing to the pi-base, and we'll be building and distributing tools to make that collaboration easier and richer.
Conventions
The historical literature isn't always consistent on notation or terms. We adhere to the following conventions:
Primary Texts
Where there is no contradiction with each other or the following conventions, we use terminology established in the following texts:
- General Topology by Stephen Willard
- Topology by James Munkres
Separation Axioms
For the separation axioms, T_n ⇒ T_m whenever n ≥ m. For example regular is defined to assert that closed points and sets can be separated; T₃ is defined to be both regular and T₀. See e.g. wikipedia for more information.
Local Properties
If a property is named "locally P", then that means that every point in the space has a neighborhood base satisfying P for every member of the base. On the other hand, some authors define "locally P" to mean there is a single neighborhood satisfying P for each point. These definitions are occasionally equivalent (e.g. locally metrizable), but are not equivalent in general (e.g. locally compact). See this issue for discussion.
Use "locally P" when there's a basis of P neighborhoods, and (when not equivalent) use "weakly locally P" when there's a single P neighborhood.