HTML special characters and symbols
If you use html, you can start a new paragraph, but putting <P> between your paragraphs.
Please choose at least one question and e-mail me the answer in either html or pdf form. If you used latex, please also e-mail me the latex file. Your answer should be as complete as possible. For example, if a property does not hold for arbitrary subspaces, does it hold for subspaces which are closed or open or etc, in the big space. If a property does not hold true for all subspaces, give counter-examples (open/closed/etc).
When you send your file, please also e-mail me the following html code: <a href="FALL08/filename"> answer </a> where answer might be yes (if holds for arbitrary), open, closed, sometimes, no, etc.
filename should be row_column.html or column_row.pdf (for example, T0_subspace.html).
If you use html, please use the following header:
<h3><a name=" row_column">A column of a row space is/is not row
</a></h3>
where instead of "A column of a row space is/is not row", use a
descriptive title.
If you are also sending a latex file, please e-mail me the following html
code:
<a href="FALL08/filename.pdf"> answer </a>
<a href="FALL08/filename.tex"> latex </a>
answer
latex
Note many of the links below are broken. I will fix that over the weekend (and check if the table below is correct).
| subspace | product | image | metric | compact Hausdorff | |
| T0 | MF | Yes | Yes | ||
| T1 | MF | Yes | Yes | ||
| T2 | MF | WY | Yes | Yes | |
| regular | Yes latex | Yes | |||
| completely regular | Yes latex | Yes | |||
| normal | MF | Yes | |||
| subspace | product | image | metric | compact Hausdorff | |
| connected | counterexample latex | JR | yes | ||
| locally connected | Open | ||||
| path connected | HJA | ||||
| locally path connected | |||||
| subspace | product | image | metric | compact Hausdorff | |
| compact | counterexample latex sometimes latex | yes | Yes | ||
| locally compact | Yes latex | ||||
| limit point compact | CG | answer answer latex | |||
| sequentially compact | KO | ||||
| Lindelof | WY | yes latex | |||
| locally compact Hausdorff | Yes latex | ||||
| subspace | product | image | metric | compact Hausdorff | |
| 2nd countable | Yes latex | YS | |||
| 1rst countable | YS | YS | |||
| separable | not necessarily, closed yes, open no latex yes latex | ||||
| metrizable | yes | ||||
| locally metrizable |