Uniform quotients of metrizable spaces
J. Vilímovský (1987)
Fundamenta Mathematicae
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J. Vilímovský (1987)
Fundamenta Mathematicae
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Roland Coghetto (2016)
Formalized Mathematics
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In this article, we formalize in Mizar [1] the notion of uniform space introduced by André Weil using the concepts of entourages [2]. We present some results between uniform space and pseudo metric space. We introduce the concepts of left-uniformity and right-uniformity of a topological group. Next, we define the concept of the partition topology. Following the Vlach’s works [11, 10], we define the semi-uniform space induced by a tolerance and the uniform space induced by an equivalence...
Michael David Rice (1977)
Czechoslovak Mathematical Journal
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Jan Hejcman, Jiří Vilímovský (1988)
Czechoslovak Mathematical Journal
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Joanne L. Walters-Wayland (1998)
Commentationes Mathematicae Universitatis Carolinae
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A locallic version of Hager’s metric-fine spaces is presented. A general definition of -fineness is given and various special cases are considered, notably all metric frames, complete metric frames. Their interactions with each other, quotients, separability, completion and other topological properties are discussed.
Lowen, Robert, Windels, Bart (1998)
International Journal of Mathematics and Mathematical Sciences
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N. C. Manna (1970)
Colloquium Mathematicae
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