Locally decodable codes (LDCs) have played a central role in many recent results in theoretical computer science. The role of finite fields, and in particular, low-degree polynomials over finite fields, in the construction of these objects is well studied. However the role of group homomorphisms in the construction of such codes is not as widely studied. Here we initiate a systematic study of l...

The study of graph homomorphisms has a long and distinguished history, with applications in many areas of graph theory. There has been recent interest in counting homomorphisms, and in particular on the question of finding upper bounds for the number of homomorphisms from a graph G into a fixed image graph H. We introduce our techniques by proving that the lex graph has the largest number of ho...

Recognizable sets of unranked, unordered trees have been introduced in Courcelle [C89] in a Myhill-Nerode [N58] style of inverse homomorphisms of suitable finite magmas. This is equivalent of being the the union of some congruence classes of a congruence of finite index. We will add to the well-known concept of regular tree grammars a handling of nodes labeled with ǫ. With this rather unconvent...

Let G be a compact Lie group with H and K arbitrary closed subgroups. Let BG, BH, BK be /-universal classifying spaces, with p{H, G): BH -» BG the natural projection. Then transfer homomorphisms J\H, G): h(BH) -» h(BG) are defined for h an arbitrary cohomology theory. One of the basic properties of the transfer for finite coverings is a double coset formula. This paper proves a double coset the...

For two not necessarily commutative topological groups G and T , let H(G, T ) denote the space of all continuous homomorphisms from G to T with the compact-open topology. We prove that if G is metrizable and T is compact then H(G, T ) is a k-space. As a consequence we obtain that if G1 is a dense subgroup of G then H(G1, T ) is homeomorphic to H(G,T ), and if G is separable h-complete, then the...

Booleanization of frames or uniform frames, which is not functorial under the basic choice of morphisms, becomes functorial in the categories with weakly open homomorphisms or weakly open uniform homomorphisms. Then, the construction becomes a reflection. In the uniform case, moreover, it also has a left adjoint. In connection with this, certain dual equivalences concerning uniform spaces and u...

It is shown that some familiar properties of epimorphisms in the category of frames cary over to the category of uniform frames. This is achieved by suitably enriching certain frame homomorphisms to uniform frame homomorphisms. This note deals with the natural question, apparently never considered so far, whether certain familiar facts concerning epimorphisms, and specifically epi-extensions, o...

Standard examples of inverse limits arise from sequences of groups, with maps between them: for instance, if we have the sequence Gn = Z/pZ for n ≥ 0, with the natural quotient maps πn+1 : Gn+1 → Gn, the inverse limit consists of tuples (g0, g1, . . . ) ∈ ∏ n≥0Gn such that πn+1(gn+1) = gn for all n ≥ 0. This is a description of the p-adic integers Zp. It is clear that more generally if the Gn a...

let x be a hypergroup. in this paper, we study the homomorphisms on certain subspaces of l(x)* which are weak*-weak* continuous.