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Hausdorff compactifications and Wallman spaces

Acta Mathematica Hungarica
Volume/Issue:
Volume 28: Issue 3-4
DOI:
https://doi.org/10.1007/bf01896785
Author: A. Sultan
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On characterization and properties of replete Wallman spaces

Periodica Mathematica Hungarica
Volume/Issue:
Volume 31: Issue 2
DOI:
https://doi.org/10.1007/bf01876486
Author: James Camacho

The subset of lattice regular zero-one valued measures on an algebra generated by a lattice (a Wallman-type space) which integrates all lattice continuous functions on an arbitrary setX is introduced and some properties of it are presented.

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On an extension of a lattice-continuous mapping with embeddability applications

Periodica Mathematica Hungarica
Volume/Issue:
Volume 16: Issue 4
DOI:
https://doi.org/10.1007/bf01848073
Authors: G. Bachman and P. Stratigos
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Repleteness and regular lattice measures

Periodica Mathematica Hungarica
Volume/Issue:
Volume 23: Issue 2
DOI:
https://doi.org/10.1007/bf02280662
Author: El-B. Yallaoui

Abstract  

Let X be an abstract set and L a lattice of subsets of X. To each lattice regular measure µ, we associate two induced measures

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\hat \mu$$ \end{document}
and
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\tilde \mu$$ \end{document}
on suitable lattices of the Wallman space IR(L) and another measure µ
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\hat \mu$$ \end{document}
,
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\tilde \mu$$ \end{document}
and µ; and try to set some new criterion for repleteness and measure repleteness.

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