Regarding arc-wise accessibility in the plane
Regular ....-classes of semigroups of continua.
Remarks on non-planable dendroids
Research Article. Multiscale Analysis of 1-rectifiable Measures II: Characterizations
A measure is 1-rectifiable if there is a countable union of finite length curves whose complement has zero measure. We characterize 1-rectifiable Radon measures μ in n-dimensional Euclidean space for all n ≥ 2 in terms of positivity of the lower density and finiteness of a geometric square function, which loosely speaking, records in an L2 gauge the extent to which μ admits approximate tangent lines, or has rapidly growing density ratios, along its support. In contrast with the classical theorems...
Rozklad elementární křivky na Jordanovy křivky