CONVENTIONS.md

Conventions for terminology on π-Base

We adhere to the following conventions:

• Where there is no contradiction, we use conventions established in the following texts:
  • General Topology by Stephen Willard
  • Topology by James Munkres
• For the separation axioms, T_n \Rightarrow T_m whenever n\geq m.
  • For example, on π-Base "regular" is defined to assert that points and closed sets can be separated, while T_3 is defined to be both regular and T_0. However, some authors swap these.
  • See e.g. https://en.wikipedia.org/wiki/Separation_axiom#Main_definitions for more information.
• If a property is "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" to mean there is a single neighborhood satisfying P for each point. This is fine for e.g. local metrizability, but is not equivalent in general, e.g. local compactness. See pi-base/data#42 for discussion. Use "locally P by single neighborhoods" instead in this case.