The main result of this paper is the following. Given countably many multivariate polynomials with rational coefficients and maximum degree d, we construct a compact set E ⊂ Rn of Hausdorff dimension n/d which does not contain finite point configurations corresponding to the zero sets of the given polynomials. Given a set E ⊂ Rn, we study the angles determined by three points of E. The main res...

In this paper, a new definition of fuzzy bounded sets and totallyfuzzy bounded sets is introduced and properties of such sets are studied. Thena relation between totally fuzzy bounded sets and N-compactness is discussed.Finally, a geometric characterization for fuzzy totally bounded sets in I- topologicalvector spaces is derived.

In this paper‎, ‎we introduce the notion of $(m,n)$-‎algebr‎aically compact modules as an analogue of algebraically‎ ‎compact modules and then we show that $(m,n)$-algebraically‎ ‎compactness‎ ‎and $(m,n)$-pure injectivity for modules coincide‎. ‎Moreover‎, ‎further characterizations of a‎ ‎$(m,n)$-pure injective module over a commutative ring are given‎.

In this paper, we investigate the concept of topological stationary for locally compact semigroups. In [4], T. Mitchell proved that a semigroup S is right stationary if and only if m(S) has a left Invariant mean. In this case, the set of values ?(f) where ? runs over all left invariant means on m(S) coincides with the set of constants in the weak* closed convex hull of right translates of f. Th...

We study labelling schemes for X-constrained path problems. Given a graph (V,E) and X ⊆ V , a path is X-constrained if all intermediate vertices avoidX. We study the problem of assigning labels J(x) to vertices so that given {J(x) : x ∈ X} for any X ⊆ V , we can route on the shortest X-constrained path between x, y ∈ X. This problem is motivated by Internet routing, where the presence of routin...

We explore representing the compact subsets of a given represented space by infinite sequences over Plotkin's T. We show that compact Hausdorff spaces with a proper dyadic subbase admit representations of their compact subsets in such a way that compact sets are essentially underspecified points. We can even ensure that a name of an n-element compact set contains at most n occurrences of ⊥.