On the Skorohod topology for functions with values in a completely regular space

TL;DR

This paper addresses a correction to a fundamental theorem regarding the Skorohod topology for functions mapping from [0,1] into a completely regular space, ensuring the mathematical rigor of the original proof.

Contribution

The authors identify and fix a gap in Jakubowski's 1986 proof concerning the Skorohod topology in a general topological setting.

Findings

Corrected the proof of Jakubowski's theorem

Ensured the validity of the Skorohod topology in completely regular spaces

Strengthened the theoretical foundation for stochastic process convergence

Abstract

We correct a gap in the proof of a basic theorem by Jakubowski (1986) on the Skorohod topology on the space of functions on [0,1] with values in a completely regular topological space.