In this paper, we give some properties of rectifiable spaces and their relationship with P-space, metrizable space. These results are used to generalize some results in [2], [9] and [12]. Moreover, we give the conditions for a rectifiable space to be second-countable.
<p>In 2009, A. I. El-Maghrabi and A. A. Nasef introduced a new class of sets between semi-closed and gs<em>-</em>closed sets called g*s-closed and gave some of their properties ([1]). In this paper, we introduce and study the concepts of three new class of maps, namely g*s<em>-</em>continuous maps, g*s<em>-</em>irresolute maps and g*s<em>-</em>closed maps. Moreover, we introduce the concepts of g*s<em>-</em>compactness of topological spaces.</p>
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