Ubiquitously Continuous on Seminorm - Rosmaya, Dwi Ajeng; Ibrahim, Nayaka; Putri, Marizcha Lutfiana; Maharani, Dian (Proceedings of the International Conference on Green Technology; Vol 14 No 1 (2024): Proceeding of 14th International Conference on Green Technology, 2024)
The term ubiquitously continuous is defined with the purpose of investigating the continuity of a linear operator based on the presence of normed spaces infinite dimensional linear subspaces. Norms and seminorms are parts of the study of normed spaces and obviously are both able to be continuous or discontinuous with respect to their spaces. Hence, this paper aims to explore how ubiquitously continuity of norms and seminorms with respect to infinite dimensional vector spaces. By using available theorems and lemmas, norms and seminorms are generally ubiquitously continuous unless the norms and seminorms themselves are discontinuous at a certain point.