Leray–Schauder and Krasnoselskii results for multivalued maps defined on pseudo-open subsets of a Fréchet space

New Leray–Schauder alternatives and Krasnoselskii expansion and compression theorems are presented for multivalued maps defined on subsets of a Fréchet space EE. The proof relies on the notion of a pseudo-open set and on viewing EE as the projective limit of a sequence of Banach spaces.