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Cofinal types of topological directed orders

SŁawomir Solecki, Stevo Todorcevic (2004)

Annales de l’institut Fourier

We investigate the structure of the Tukey ordering among directed orders arising naturally in topology and measure theory.

Locally solid topological lattice-ordered groups

Liang Hong (2015)

Archivum Mathematicum

Locally solid Riesz spaces have been widely investigated in the past several decades; but locally solid topological lattice-ordered groups seem to be largely unexplored. The paper is an attempt to initiate a relatively systematic study of locally solid topological lattice-ordered groups. We give both Roberts-Namioka-type characterization and Fremlin-type characterization of locally solid topological lattice-ordered groups. In particular, we show that a group topology on a lattice-ordered group is...

Means on scattered compacta

T. Banakh, R. Bonnet, W. Kubis (2014)

Topological Algebra and its Applications

We prove that a separable Hausdor_ topological space X containing a cocountable subset homeomorphic to [0, ω1] admits no separately continuous mean operation and no diagonally continuous n-mean for n ≥ 2.

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