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• CommentRowNumber1.
• CommentAuthormaxsnew
• CommentTimeSep 25th 2019

The table on the separation axioms page looks very messed up. If I open the table directly at main separation axioms – table it looks fine but on the separation axioms page, all of the links are gone. How do we fix it?

• CommentRowNumber2.
• CommentAuthorRichard Williamson
• CommentTimeSep 25th 2019
• (edited Sep 25th 2019)

I re-rendered (made a trivial edit to) the table page, the other page looks fine now I think. This was probably a relic of the teething issues with the change in renderer last year.

• CommentRowNumber3.
• CommentAuthormaxsnew
• CommentTimeSep 26th 2019

Great! thanks

1. I added to the introduction a couple of remarks mentioning separation axioms in terms of lifting properties with respect to finite topological spaces (i.e. preorders).

Also, I noted that the page mentioned but did not define Axiom T5, so I made a change making it clear it means “completely normal” (=heriditarily normal).

Anonymous

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeSep 23rd 2021

Where the paragraph ends with:

… i.e. the function determined by two distinct points is not continuous as a map from the indiscrete space.

I feel that a conclusion is missing that explicitly explains the promised lifting.

Not having looked at how this works, I gather the sentence could be completed as:

…or concersely: Every continuous such function necessarily factors through the point space.

But that would be an “extension property”, not a lifting property. (?)

(I understand that I will find this explained in more detail in the entry on separation by lifting, and I’ll look at that when I have more leisure. But just to mention that the idea section here could make this clearer.)

2. Where the paragraph ends with:

… i.e. the function determined by two distinct points is not continuous as a map from the indiscrete space.

I feel that a conclusion is missing that explicitly explains the promised lifting.

…or concersely: Every continuous such function necessarily factors through the point space.

But that would be an “extension property”, not a lifting property. (?)

Correct. But an extension property is a form of a lifting property. Now I write the lifting properties for T0, T1, and T2 explicitly, although in a rather verbose manner.

(I understand that I will find this explained in more detail in the entry on separation by lifting, and I’ll look at that when I have more leisure. But just to mention that the idea section here could make this clearer.)

The chief difficulty there is introducing notation for maps of preorders (equivalently, maps of finite topological spaces)….

Anonymous

3. I included diagrams for separation axioms T0-T4 as lifting properties with respect to morphisms of finite topological settings. One should probably fix the typesetting and put diagrams next to each other, not below each other. I hope the diagrams are self-explanatory, with remarks provided.

Anonymous

• CommentRowNumber8.
• CommentAuthorGuest
• CommentTimeApr 14th 2022

There’s a spelling error in the section “Beyond the classical theory”:

The space is $T_1$ if and only if the sepcification order is the equality relation.

• CommentRowNumber9.
• CommentAuthorzskoda
• CommentTimeSep 3rd 2022

Clicking on the reference

• {#Naik} Vipul Naik, Topology: The journey into separation axioms (pdf)

listed in separation axioms results in

Forbidden

You don’t have permission to access this resource.

• CommentRowNumber10.
• CommentAuthorUrs
• CommentTimeSep 4th 2022

Not sure what to make of this comment. It sounds like you don’t know the following, so let me just say it:

This is a phenomenon called “link rot”. When you come across it on the nLab, the first best thing to do is to google the document name to see under which URL it is available meanwhile. If Google can’t find any current copy, then in most cases handing the broken link to the WaybackMachine serves to produce the file.

Once a working link is recovered, it’s straightforward to fix the broken link on the nLab using it. Better yet, to prevent that the fixed link eventually rots away itself: Upload the file to the nLab server itself.

That’s what I have done in the present case, the file is now at ncatlab.org/nlab/files/Naik-SeparationAxioms.pdf (and as such linked to from the nLab page here).

• CommentRowNumber11.
• CommentAuthorUrs
• CommentTimeSep 24th 2022

to the section on $T_n$-reflections I have added pointer to:

• Horst Herrlich, George Strecker, Categorical topology – Its origins as exemplified by the unfolding of the theory of topological reflections and coreflections before 1971 (pdf), pages 255-341 in: C. E. Aull, R Lowen (eds.), Handbook of the History of General Topology. Vol. 1, Kluwer 1997 (doi:10.1007/978-94-017-0468-7)
4. Fixing spelling error

Anonymous

5. Adding disambiguation message to top of page

Anonymous