Abstract This paper investigates four classes of functions with a single discontinuous point. We give the sufficient and necessary conditions under which the second order iterates are continuous ...

Activation functions provide the non-linearity to deep neural networks, which are crucial for the optimization and performance improvement. In this paper, we propose a learnable continuous piece-wise ...

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 ...

D. C. Gillespie, W. A. Hurwitz, On Sequences of Continuous Functions Having Continuous Limits, Transactions of the American Mathematical Society, Vol. 32, No. 3 (Jul ...