New results regarding the lattice of uniform topologies on C(X).

For a Tychonoff space X, the lattice UX was introduced in L. A. Pérez-Morales, G. Delgadillo-Piñón, and R. Pichardo-Mendoza, The lattice of uniform topologies on C(X), Questions and Answers in General Topology 39 (2021), 65-71. In the present paper we continue the study of UX. To be specific, the present paper deals, in its first half, with structural and categorical properties of UX, while in its second part focuses on cardinal characteristics of the lattice and how these relate to some cardinal functions of the space X. [ABSTRACT FROM AUTHOR]