The Bunyakovsky conjecture (or Bouniakowsky conjecture) stated in 1857 by the Russian mathematician Viktor Bunyakovsky, asserts when a polynomial in one variable with positive degree and integer coefficients should have infinitely many prime values for positive integer inputs. Three necessary conditions are the leading coefficient of is positive, the polynomial is irreducible over the integers, and as runs over the positive integers, the numbers should be relatively prime. (Thus, the coefficients of should be relatively prime.) Bunyakovsky's conjecture is that these three conditions ar...

In the mathematical field of general topology, a Dowker space is a topological space that is T4 but not countably paracompact. They are named after Clifford Hugh Dowker. The non-trivial task of providing an example of a Dowker space (and therefore also proving their existence as mathematical objects) helped mathematicians better understand the nature and variety of topological spaces. Topological spaces are sets together with some subsets (designated as "open sets") satisfying certain properties. Topological spaces arose as generalization of the open sets of spaces studied in elementary mathematics...