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Add "iff Kolmogorov ..." for most remaining properties#1725

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felixpernegger wants to merge 2 commits intomainfrom
kolmoquotient
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Add "iff Kolmogorov ..." for most remaining properties#1725
felixpernegger wants to merge 2 commits intomainfrom
kolmoquotient

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@felixpernegger
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@felixpernegger felixpernegger commented Apr 4, 2026

Add "property holds iff for kolmogorov quotient" for almost all proerties where it is true. For weakly first countable for example, it could be true.

This is kind of a big PR, but most of the additions are trivial or at least easy (similar to #1674). I dont think it makes sense to artificially split this up.
Most of the addtions are originally by @danflapjax in his spreadsheet in #1198, which I expanded.

It's plausible there are some mistakes (sometimes taking the quotient can be confusing, i.e. for Sequential), so please check carefully.

(as you might can guess I used AI to get the data from the spreadsheet to the property files)

@prabau
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prabau commented Apr 4, 2026

Are all these additions with "iff", or are there some implications in only one direction?

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Are all these additions with "iff", or are there some implications in only one direction?

All the ones I added to the spreadsheet are "iff", I cant speak for the old ones but I suspect the same.

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prabau commented Apr 4, 2026

If I remember correctly, the existing ones had some cases where only one implication was valid; don't remember which ones right now. There are also cases when the properties are not the same for $X$ and $Kol(X)$, for example pseudometrizable and metrizable.

@felixpernegger
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If I remember correctly, the existing ones had some cases where only one implication was valid; don't remember which ones right now. There are also cases when the properties are not the same for X and K o l ( X ) , for example pseudometrizable and metrizable.

I think you are right. I checked which of the properties changed imply T0 and it was only P46 (for which I removed the kolmogorov metaprop now). The rest is probably fine then.

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