A diagonal principle for nets

Abstract

In our work, we provide a constructive proof of a generalized version of Cantor's diagonal argument for nets. This result expands the well-known technique beyond sequences, allowing it to be applied to a broader context. This result has significant potential applications in various fields, and we demonstrate a few of these in our work. One such application is the solution to a previously open problem posed by Kandi\'c, Marabeh, and Troitsky. Specifically, we show that the set of unbounded norm compact operators from a Banach space to a Banach lattice is closed.