  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.
