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### Variously pointed closed sets

A tree $A\subseteq \omega^{<\omega}$ - possibly with dead ends - is pointed iff every path $p\in[A]$ has $p\ge_TA$. This lifts to two distinct notions of pointedness for closed sets in Baire space: ...
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### Reference: Hajlasz-Sobolev Spaces with Values in a Metric Space

Let $(X,d,\mu)$ be a separable metric measure space on which every ball has positive but finite measure. I've come across the definition of a homogeneous Fractional Hajlasz-Sobolev spaces which are ...
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### Volume doubling, uniform Poincaré, counterexample

The Poincaré inequality and the volume doubling property are important notions related to heat kernel estimates. Pavel Gyrya and Laurent Saloff-Coste obtain the two sided heat kernel estimate of ...
Let $CDGA$ be the category of commutative differential graded algebras over a field $k$ of characteristic zero. Denote by $\Omega\left(\Delta^n\right)$ the cdga of algebraic differential forms on the \$...