A Selection Principle and Products in Topological Groups

We consider the preservation under products, finite powers, and forcing of a selection-principle-based covering property of T₀ topological groups. Though the paper is partly a survey, it contributes some new information: (1) The product of a strictly o-bounded group with an o-bounded group is an o-bounded group—Corollary 1. (2) In the generic extension by a finite support iteration of ℵ₁ Hechler reals the product of any o-bounded group with a ground model ℵ₀ bounded group is an o-bounded group—Theorem 11. (3) In the generic extension by a countable support iteration of Mathias reals the product of any o-bounded group with a ground model ℵ₀ bounded group is an o-bounded group—Theorem 12.