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math.GN2020★ 2 cited
Simultaneous Extension of Continuous and Uniformly Continuous Functions
Valentin Gutev
The first known continuous extension result was obtained by Lebesgue in 1907. In 1915, Tietze published his famous extension theorem generalising Lebesgue's result from the plane t…
math.GN2020
Weak Selections and Suborderable Metrizable Spaces
Valentin Gutev
Each continuous weak selection for a space defines a coarser topology on , called a selection topology. Spaces whose topology is determined by a collection of such selection…
math.GN2020
Lipschitz Extensions and Approximations
Valentin Gutev
The classical Hahn-Banach theorem is based on a successive point-by-point procedure of extending bounded linear functionals. In the setting of a general metric domain, the conditio…