Monotone extenders for bounded c-valued functions

• Autorzy: Kaori Yamazaki
• Języki publikacji: EN

Abstrakty

EN

Let c be the Banach space consisting of all convergent sequences of reals with the sup-norm, $C_{∞}(A,c)$ the set of all bounded continuous functions f: A → c, and $C_{A}(X,c)$ the set of all functions f: X → c which are continuous at each point of A ⊂ X. We show that a Tikhonov subspace A of a topological space X is strong Choquet in X if there exists a monotone extender $u: C_{∞}(A,c) → C_{A}(X,c)$. This shows that the monotone extension property for bounded c-valued functions can fail in GO-spaces, which provides a negative answer to a question posed by I. Banakh, T. Banakh and K. Yamazaki.

Kategorie tematyczne

• 46A40: Ordered topological linear spaces, vector lattices
• 91A44: Games involving topology or set theory
• 46A55: Convex sets in topological linear spaces; Choquet theory
• 54F05: Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
• 54C20: Extension of maps
• 46B40: Ordered normed spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2010
• Tom: 199
• Numer: 1
• Strony: 17-22

Daty

wydano

2010

Twórcy

autor

Kaori Yamazaki

• Faculty of Economics, Takasaki City University of Economics, 1300 Kaminamie, Takasaki, Gunma 370-0801, Japan

Identyfikatory

DOI

10.4064/sm199-1-2