Let $X$ be a set, $A$ a family of real-valued functions on $X$ which contains the constants, $\mu_A$ the weak uniformity generated by $A$, and $U(\mu_AX)$ the ...

We show that the lateral regularizations of the generator of any uniformly bounded set-valued composition Nemytskij operator acting in the spaces of functions of bounded variation in the sense of ...

Abstract: Questions of uniform approximation of continuous functions of bounded variation on ℝ n with the values in the Banach space are being studied by aggregates of summatory type constructed on ...

Atsuji has internally characterized those metric spaces X for which each real-valued continuous function on X is uniformly continuous as follows: (1) the set X' of limit points of X is compact, and (2 ...

Due to a planned power outage on Friday, 1/14, between 8am-1pm PST, some services may be impacted. A line drawing of the Internet Archive headquarters building façade. An illustration of a magnifying ...

Abstract: The theorem of V.I. Zubov about the possibility of uniform approximation on the all real axis for an arbitrary continuous distribution function with using approaching aggregates built on the ...

Properties of the real numbers, infimum and supremum of sets. Numerical sequences and series. Limits of functions, continuous functions, intermediate value theorem, uniform continuity. Differentiation ...