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- W1942163404 abstract "The concept of the tight extension of a metric space was introduced and studied by Dress. It is known that Dress theory is equivalent to the theory of the injective hull of a metric space independently discussed by Isbell some years earlier. Dress showed in particular that for a metric space <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M1><mml:mrow><mml:mi>X</mml:mi></mml:mrow></mml:math> the tight extension <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M2><mml:mrow><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>X</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math> is maximal among the tight extensions of <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M3><mml:mrow><mml:mi>X</mml:mi></mml:mrow></mml:math>. In a previous work with P. Haihambo and H.-P. Künzi, we constructed the tight extension of a <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M4><mml:mrow><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant=normal>0</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>-quasi-metric space. In this paper, we continue these investigations by presenting a similar construction in the category of <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M5><mml:mi>U</mml:mi><mml:mi>Q</mml:mi><mml:mi>P</mml:mi></mml:math>-metric spaces and nonexpansive maps." @default.
- W1942163404 created "2016-06-24" @default.
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- W1942163404 date "2015-09-30" @default.
- W1942163404 modified "2023-09-26" @default.
- W1942163404 title "Ultra-Quasi-Metrically Tight Extensions of Ultra-Quasi-Metric Spaces" @default.
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- W1942163404 doi "https://doi.org/10.1155/2015/646018" @default.
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