Some remarks on Pseudocompactness

Résumé

In this paper, we introduced the notion of $d_{G}$-pseudocompactness of topological spaces with respect to some metric space $(G, d)$ and we gave characterization for a topological space to be $d_{G}$-pseudocompact with respect to some metric group $(G, d)$. We investigated the relationship of $d_{G}$-pseudocompactness with other types of compactness and found some conditions under which the notion of $d_{G}$-pseudocompactness becomes equivalent to pseudocompactness.