Collectionwise normality and extensions of continuous functions
T. Przymusiński (1978)
Fundamenta Mathematicae
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Displaying similar documents to “Continuous extenders in normal and collectionwise normal spaces”
Collectionwise normality and extensions of continuous functions
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We investigate isomorphic embeddings T: C(K) → C(L) between Banach spaces of continuous functions. We show that if such an embedding T is a positive operator then K is the image of L under an upper semicontinuous set-function having finite values. Moreover we show that K has a π-base of sets whose closures are continuous images of compact subspaces of L. Our results imply in particular that if C(K) can be positively embedded into C(L) then some topological properties of L, such...
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Does a given Banach space have any non-trivial complemented subspaces? Usually, the answer is: yes, quite a lot. Sometimes the answer is: no, none at all.