quasi-uniformisation of bitopological spaces

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By a well-known result of Pervin every topological space is quasi-uniformisable. Since a quasi-uniformity always induces two topologies, one naturally obtains from a quasi-uniform space a bitopological space. Are there known conditions which characterise those bitopological spaces that arise from a quasi-uniform space? In other words, let $Fcolon QUnif to BTop$ be the evident functor assigning a bitopological space to a quasi-uniform space. Can one characterise the essential image of $F$ in terms of the given topologies comprising a bitopological space?




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    By a well-known result of Pervin every topological space is quasi-uniformisable. Since a quasi-uniformity always induces two topologies, one naturally obtains from a quasi-uniform space a bitopological space. Are there known conditions which characterise those bitopological spaces that arise from a quasi-uniform space? In other words, let $Fcolon QUnif to BTop$ be the evident functor assigning a bitopological space to a quasi-uniform space. Can one characterise the essential image of $F$ in terms of the given topologies comprising a bitopological space?




    general-topology uniform-spaces




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      By a well-known result of Pervin every topological space is quasi-uniformisable. Since a quasi-uniformity always induces two topologies, one naturally obtains from a quasi-uniform space a bitopological space. Are there known conditions which characterise those bitopological spaces that arise from a quasi-uniform space? In other words, let $Fcolon QUnif to BTop$ be the evident functor assigning a bitopological space to a quasi-uniform space. Can one characterise the essential image of $F$ in terms of the given topologies comprising a bitopological space?




      general-topology uniform-spaces




      share|cite|improve this question













      By a well-known result of Pervin every topological space is quasi-uniformisable. Since a quasi-uniformity always induces two topologies, one naturally obtains from a quasi-uniform space a bitopological space. Are there known conditions which characterise those bitopological spaces that arise from a quasi-uniform space? In other words, let $Fcolon QUnif to BTop$ be the evident functor assigning a bitopological space to a quasi-uniform space. Can one characterise the essential image of $F$ in terms of the given topologies comprising a bitopological space?





      general-topology uniform-spaces





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      edited Jul 30 at 17:02









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      asked Jul 30 at 16:06









      Ittay Weiss

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      This question had a bounty worth +500
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