Talk:Finite intersection property

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Finite intersction axiom

Latest comment: 19 years ago1 comment1 person in discussion

Some definitions of compactness invoke the finite intersection axiom, related to axiom of choice by Tychonoff's theorem; the relationship is not clear to me just right now. I guess this is an article request. linas 02:16, 21 November 2005 (UTC)Reply

Merge with centered system of sets

Latest comment: 15 years ago2 comments2 people in discussion

Yesterday I wrote an article about the definition of centered system of sets. Today I saw that it has been proposed to be merged with this article, since the two notions are the same.

I don't know how the two terms emerged. The term centered system of sets seams to be uncommon in English literature and my guess is that it originated in Russian and found it's way into English books through translations.

I am willing to do the merging. How should the merger of two definitions in mathematics go? Create a section in the destination article about the alternative naming?

Sogartar (talk) 07:42, 4 February 2010 (UTC)Reply

There wasn't any useful information at centered system of sets, so I've redirected it and added a note at the top of this article mentioning the definition—so perhaps technically a merge, but nothing was copied over. xnn (talk) 22:28, 24 February 2010 (UTC)Reply

Grammar

Is "has non-empty intersection" proper English, or should it be "has a non-empty intersection"?

Why not the empty family?

Latest comment: 39 minutes ago1 comment1 person in discussion

At multiple points in the article we define or require that the family (or collection) A of sets must have at least one set in order to try to satisfy the finite intersection property. But I don't see any statements that fail to be true if that condition is removed. Occam's razor would seem to tell us that if we don't need to require that the family A be non-empty then we should remove that condition. —Quantling (talk | contribs) 18:18, 27 August 2025 (UTC)Reply