All Questions

Do you know any (standard) name for a function $f:\mathbb R\to\mathbb R$ having the following weak intermediate value property: $(*)$ for any connected subset $C\subset \mathbb R$ and points $a,b\...

A coauthor and I have stumbled upon a useful topological property -- namely, we are interested in the property that every nonempty closed set contains a closed point. However, neither of us are ...

Let $X$ be a subset of a topolgical space with no open points. Then $$\overline{X}=X_1\sqcup X_2\sqcup X_3\sqcup X_4\sqcup X_5$$ where $X_1$ are isolated points of $X$, $X_2$ are interior points, $X_3=...

Recall: given a (possibly non-$T_0$) topological space $X$, its Kolmogorov quotient $KX$ is the $T_0$ topological space formed by $X/\sim$ where $x\sim y$ if they are topologically indistinguishable. ...

According to @Tyrone the term well-embedded set was first used in Measures on Metacompact Spaces by W. Moran. In the article Extensions of Zero-sets and of Real-valued Functions by R. Blair and A. ...

Let $M$ be a (not necessarily Hausdorff) smooth manifold. Given an open chart $U\subset M$ and a compactly-supported smooth function $f:U\to\mathbb{R}$ on $U$, define $\widetilde{f}:M\to\mathbb{R}$ by ...