$top$-filters can be used to define $top$-convergence spaces in the lattice-valued context. Connections between $top$-convergence spaces and lattice-valued convergence spaces are given. Regularity of a $top$-convergence space has recently been defined and studied by Fang and Yue. An equivalent characterization is given in the present work in terms of convergence of closures of $top$-filters.  M...

We study linear filters for processing signals supported on abstract topological spaces modeled as simplicial complexes, which may be interpreted generalizations of graphs that account nodes, edges, triangular faces, etc. To process such signals, we develop convolutional defined matrix polynomials the lower and upper Hodge Laplacians. First, properties these show they are shift-invariant, well ...