Talk:Metrizable space

Manifolds
Not actually relevant to the page, but does anyone know if there is are similar theorems about when a topological space is homeomorphic to a manifold?

Submetrizablity
I am pretty sure that that the space is submetrizable means that it contains a metrizable subspace or the space is homeomorphic to such a space, but I couldn't find (by means of quick google search) a reference to back this. Does anyone confirm this? Without defining Submetrizablity we can't go deep into the metrizable problems in my opinion. -- Taku 03:40, 3 March 2007 (UTC)

A space is called submetrizable if it has a weaker metrizable topology. The Sorgenfrey line is an example: the usual topology on R is a weaker and metrizable topology.Hennobrandsma 14:01, 2 June 2007 (UTC)

Separation Axioms
Most texts, Dugundji being an example, consider normality to be a stronger separation axiom than regularity, not weaker. But then this is normality as $$T_{4}$$, and regularity as $$T_{3}$$. Without some clarification in this article, it isn't clear what Urysohn actually said. Further, this article needs style editing--or is it just me who thinks articles on general topology should avoid sounding flippant? 198.54.202.102 (talk) —Preceding comment was added at 15:14, 3 June 2008 (UTC)

Tychonoff's vs. Urysohn version
Under Tychonoff's assumptions X is in fact normal: second-countable implies Lindelöf, and Lindelöf + regular implies normal (this is Tychonoff's lemma). Tychonoff's contribution (his Lemma) was therefore more general than to just extend Urysohn's Metrization Theorem. — Preceding unsigned comment added by 128.32.45.74 (talk) 20:54, 24 October 2012 (UTC)

Definition
Hi guys, I'm a bit unclear on what the $$\tau$$ in the tuple $$(X,\tau)$$ is; can anyone shed some light on this? Do we approach this bracketed form similar to tuples in measure theory? thanks. 174.3.155.181 (talk) 20:28, 16 June 2016 (UTC)
 * Assuming you are referring to the lead: $$\tau$$ refers to the topology on the space $$X$$ under consideration. I hope this helps clarify. Definitely add in clarification to the text if you think this is unclear. Zfeinst (talk) 22:32, 16 June 2016 (UTC)

"Semi-metrizable" not defined
Semi-metrizable/Semi-metrisable/Semimetrizeable redirect to Metrizable space (they used to redirect to Metrization theorem before that page was moved to Metrizable space), but semi-metrizability is not defined at the target page, and apparently never was, at least I didn't find it in the article history. Can someone please add the definition? Thanks! – Tea2min (talk) 11:27, 8 April 2020 (UTC)