Boundedness in Cp(X,Y) and equicontinuity

Let G be a locally compact abelian group. Some time ago Trigos-Arrieta, improving a well-known theorem by Glicksberg, showed in a simple way that any relatively pseudocompact subset A of G+ is relatively compact in G . In the present paper, one of our aims is to point out another natural proof of Trigos-Arrietaʹs theorem which yields a stronger result. To get this result, we first establish (in terms of function spaces) an extension of Namiokaʹs theorem on separate and joint continuity (Theorem 3.4). One also finds the following application of Theorem 3.4 which substantially betters recent results by Korovin and Reznichenko: Let G be a pseudocompact Tychonoff group with separately continuous multiplication; if G is ( σ−β )-defavorable, then multiplication in G is continuous.