Quite often we have situation that discussion about a specific tag results in consensus that the tag should be removed. And the removal process means that the questions having that tag are retagged and thus bumped. In som cases, this might be quite a big number of questions. (For example, when th...
In the metric space $(Z,d)$, let $A(z_0,\varepsilon)$ denote the closed ball$\left\lbrace z\mid d(z,z_0)\leq\varepsilon\right\rbrace$. Now let $X$ be an arbitrary space, let $Y$ a metric space and let $f:X \times Y \rightarrow Z$ be continuous in each variable separately. Let $\varepsilon>0$ and ...
I thought about this idea, and come to the following two conclusions.
1. Tags for upper and lower semicontinous maps are needed to concentrate attention of these sufficiently known notions, and I think this topic is sufficiently specific and far from ‘continuity’ tag.
2. I chose to create a separate tag for upper semicontinuity’, because sometimes upper and lower cases may need different approaches (for instance, for the maps to a space $\operatorname{exp} X$ endowed with “partial” Vietoris topology) or a question may be relevant to only one of th…
The tag upper-semicontinuity was created recently, here you can see a short discussion between me and the tag-creator. From this discussion it seems that the tag is intended both for functions and multifunctions. And also that the tag-creator would prefer to have separate tags for lower and upper...
In the book of General Topology by Munkres, at page 100, it is asked to prove that Every simply ordered set is a Hausdorff space in the order topology.The product of two Hausdorff space is again a Hausdorff space. Proof of the first statement: Let X be a topological space with the ord...
On the last question: no there should be no synonym from hausdorff-spaces to separation-axioms. The issue is that somebody asking about a problem that happens to be placed in the context of a Hausdorff space might well use the former tag, while the question is not at all about separation axiom...
I don’t think that there should be a countability-axioms tag in the first place: it’s not a natural category. Second countability, first countability, and separability are just names for the countable cases of the cardinal functions weight, character, and density, respectively. If we do have it, ...
« first day (1988 days earlier) ← previous day next day → last day (2346 days later) »