This work is motivated by the problem of finding locally compact group topologies for piecewise full groups (a.k.a.~ topological groups). We determine that any in compact-open topology on self-homeomorphisms Cantor set must be uniformly discrete, a precise sense we introduce here. Uniformly discrete are particular countable, finite, residually finite and topology. The resulting form subclass am...

It is well-known that there a Sobolev homeomorphism f∈W1,p([−1,1]n,[−1,1]n) for any p<n which maps set C of zero Lebesgue n-dimensional measure onto positive measure. We study the size this critical and characterize its lower upper bounds from perspective Hausdorff measures defined by general gauge function.

Background: Hyperspectral image analysis is a fast and non-destructive technique that is being used to measure quality attributes of food products. This research investigated the feasibility of predicting internal quality attributes, such as Total Soluble Solids (TSS), pH, Titratable Acidity (TA), and maturity index (TSS/TA); and external quality attributes such as color components (L*, a*, b*)...

Topological measures and quasi-linear functionals generalize linear functionals. We define study deficient topological on locally compact spaces. A measure a space is set function open closed sets which finitely additive sets, inner regular outer sets. Deficient measures. First we investigate positive, negative, total variation of signed that only assumed to be These variations turn out Then ex...