Näytetään aineistoja, joilla on samankaltainen nimeke tai asiasanat.

• Separaatioaksioomat ja jatkuvien kuvausten laajentaminen 

  Timonen, Joel (2023)

  Tässä matematiikan Pro Gradu -tutkielmassa todistetaan McShanen ja Tietzen jatkolauseet sekä Urysonin lemma. Ensimmäinen tulos liittyy metrisiin avaruuksiin ja kaksi jälkimmäistä topologiaan. McShanen jatkolause kertoo, ...

• Vector calculus on weighted reflexive Banach spaces 

  Pasqualetto, Enrico; Rajala, Tapio (Springer Nature, 2024)

  We study first-order Sobolev spaces on reflexive Banach spaces via relaxation, test plans, and divergence. We show the equivalence of the different approaches to the Sobolev spaces and to the related tangent bundles.

• The Choquet and Kellogg properties for the fine topology when p=1 in metric spaces 

  Lahti, Panu (Elsevier Masson, 2019)

  In the setting of a complete metric space that is equipped with a doubling measure and supports a Poincar´e inequality, we prove the fine Kellogg property, the quasi-Lindel¨of principle, and the Choquet property for the ...

• A new Cartan-type property and strict quasicoverings when P = 1 in metric spaces 

  Lahti, Panu (Suomalainen tiedeakatemia, 2018)

  In a complete metric space that is equipped with a doubling measure and supports a Poincaré inequality, we prove a new Cartan-type property for the fine topology in the case p = 1. Then we use this property to prove the ...

• Singular quasisymmetric mappings in dimensions two and greater 

  Romney, Matthew (Academic Press, 2019)

  For all n ≥2, we construct a metric space (X, d)and a quasisymmetric mapping f:[0, 1]n→X with the property that f−1 is not absolutely continuous with respect to the Hausdorff n-measure on X. That is, there exists a Borel ...