Authorship attribution is a task that aims to identify the author of a given piece of writing. We aim to develop a generalized solution that can handle a large number of texts from authors and topics unavailable in training data. Previous studies have proposed strategies to address only either unseen authors or unseen topics. Authorship representation learning has been shown to work in open-set environments with a large number of unseen authors but has not been explicitly designed for cross-topic environments at the same time. To handle a large number of unseen authors and topics, we propose Authorship Representation Regularization (ARR), a distillation framework that creates authorship representation with reduced reliance on topic-specific information. To assess the performance of our framework, we also propose a cross-topic-open-set evaluation method. Our proposed method has improved performances in the cross-topic-open set setup over baselines in 4 out of 6 cases.