Talk:Cofiniteness

Compactness of the cofinite topology

Isn't a space with the cofinite topology quasicompact but not compact since it is not Hausdorff? — Preceding unsigned comment added by 73.50.103.143 (talk) 05:35, 22 June 2020 (UTC)[reply]

Cocountable

Ooops, yes I just realized I made a big mistake, am cleaning up now (I confused finite with countable, here) linas 20:07, 19 November 2005 (UTC)[reply]

Never mind. I thought I snuck in cocountable in there by accident, but I guess not. linas 21:30, 19 November 2005 (UTC)[reply]

Pathwise connected

Does anyone know whether the natural numbers with the cofinite topology are pathwise connected? --131.234.106.197 (talk) 15:42, 19 November 2009 (UTC)[reply]

It's not path-connected (all paths are constant). --Zundark (talk) 19:27, 4 March 2011 (UTC)[reply]

Split

The section on the cofinite topology occupies about half the article, making the article rather unbalanced. I suggest splitting this off into a separate cofinite topology article. --Zundark (talk) 19:27, 4 March 2011 (UTC)[reply]

Finiteness of cofinite sets

Can cofinite sets be themselves finite? From the definition it follows that they can, but this seems like it would be a degenerate case.

Example: Given {1,2,3,4}, is {1,2}, the compliment of the finite set {3,4}, cofinite? 173.173.74.129 (talk) 05:15, 10 July 2013 (UTC)[reply]

Cofinite sets in X iff X is T_1

"In fact, an arbitrary topology on X satisfies the T1 axiom if and only if it contains the cofinite topology." This doesn't seem correct to me. Mathguy9109 (talk) 17:57, 5 October 2019 (UTC)[reply]