ИСТИНА

Let G,H be locally compact groups equipped with fixed two-side invariant Haar measures. A polyhomomorphism G→H is a pair – subgroup Γ in the product G×H, – a Haar measure on Γ whose projections to G and H are dominated by the Haar measures on G and H. The set of all polyhomomorphisms G→H is a compact set with respect to the Shabauty topology. Polyhomomorphisms form a category, i.e., there is a well-defined product of polyhomomorphisms G1→G2 and G2→G3. We discuss some properties of such objects and an example (polyendomorphisms of locally compact linear spaces over finite fields).