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Unbounded convergences in vector lattices

  • Author / Creator
    Taylor, Mitchell A.
  • Suppose $X$ is a vector lattice and there is a notion of convergence $x{\alpha} \xrightarrow{\sigma} x$ in $X$. Then we can speak of an ``unbounded" version of this convergence by saying that $x{\alpha} \xrightarrow{u\sigma} x$ if $\lvert x\alpha-x\rvert \wedge u\xrightarrow{\sigma} 0$ for every $u \in X+$. In the literature the unbounded versions of the norm, order and absolute weak convergence have been studied. Here we create a general theory of unbounded convergence, but with a focus on $uo$-convergence and those convergences deriving from locally solid topologies. We also give characterizations of minimal topologies in terms of unbounded topologies and $uo$-convergence. At the end we touch on the theory of bibases in Banach lattices.

  • Subjects / Keywords
  • Graduation date
    Spring 2019
  • Type of Item
    Thesis
  • Degree
    Master of Science
  • DOI
    https://doi.org/10.7939/r3-vq30-xr62
  • License
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