Definition talk:Sigma-Locally Finite Basis

Sigma-Locally Finite Basis and Countably Locally Finite Basis

Steen and Seebach define a $\sigma$-locally finite base to be a base that is the countable union of locally finite families.

Kelley defines a $\sigma$-locally finite base to be the countable union of locally finite subfamilies.

Willard defines a $\sigma$-locally finite base to be the countable union of locally finite collections.

Muncres defines a countably locally finite basis to be the countable union of locally finite collections.

So a $\sigma$-locally finite basis is also known as a countably locally finite basis.

The $\mathsf{Pr} \infty \mathsf{fWiki}$ definition of $\sigma$-locally finite base requires each collection of the countable union to be a cover. I believe this to be unnecessary. I think this has come about because Steen and Seebach define a locally finite cover but do not define a locally finite family even though this is what their definition of $\sigma$-locally finite base requires. --Leigh.Samphier (talk) 09:57, 6 February 2023 (UTC)

Would you be in a position to rationalise this? --prime mover (talk) 17:07, 6 February 2023 (UTC)

That is my intention. I'm justifying some of the changes that I thnk are required, so that there will be no surprises. --Leigh.Samphier (talk) 07:22, 7 February 2023 (UTC)