The porous, gas permeable layer substructure (5; 5a, 5b) for a thin, gas tight layer (89) can in particular be used as a functional component in high temperature fuel cells (8). This layer substructure has a smooth surface (50a) which is suitable for an application of the gas tight layer or a multi-layer system including the gas tight layer, with the application being carried out by means of a screen printing method or other coating methods. The smooth surface is formed by a compacted edge zone (50). The edge zone and a carrier structure (51) adjacent to this are made from sinterable particles of a uniform substance mixture. The porosity of the carrier structure is greater than 30 volume percent, preferably greater than 40 volume percent. The pore size of the edge zone is smaller than 10 .mu.m, preferably smaller than 3 .mu.m.