Source: wikibot/dawson-gartner-theorem
= Dawson–Gärtner theorem
{wiki=Dawson–Gärtner_theorem}
The Dawson–Gärtner theorem is a result in the field of topology that deals with the relationship between compact spaces and their continuous images. It specifically addresses the conditions under which a continuous image of a compact space is also compact. The theorem states that if \\(X\\) is a compact space and \\(f : X \\to Y\\) is a continuous function, then the image \\(f(X)\\) is compact in \\(Y\\).