Note on certain s-dimensional sets

A note on three dimensional good sets

Department of Mathematics, Periyar University, Salem 636011, India E-mail: [email protected] 2000 Mathematics Subject Classification: primary 60A05, 47A35, secondary 28D05, 37Axx Abstract:. We show that as in the case of nfold Cartesian product for n ≥ 4, even in 3-fold Cartesian product, a related component need not be full component.

A Note on Artinianess of Certain Generalized

Let ?: R0?R be a ring homomorphism and suppose that a and a0, respectively, are ideals of R and R0 such that is an Artinian ring. Let M and N be two finitely generated R-modules and suppose that (R0,m0) is a local ring. In this note we prove that the R-modules and are Artinian for all integers i and j, whenever and . Also we will show that if a is principal, then the R-modules and ...

Note on Certain Orthogonal Polynomials

A Note on P-sets

A P-set is a set S of positive integers such that no element of S divides the sum of any two (not necessarily being different) larger elements. Erdös and Sárközy [2] conjectured that there exists a constant c > 0 such that for every P-set S we have |{s ∈ S : s ≤ N}| < N1−c for infinitely many integers N . For P-sets S consisting of pairwise coprime integers this conjecture has been proved by T....

A Note on Discrete Sets

We give several partial positive answers to a question of Juhász and Szentmiklóssy regarding the minimum number of discrete sets required to cover a compact space. We study the relationship between the size of discrete sets, free sequences and their closures with the cardinality of a Hausdorff space, improving known results in the literature.