This paper deals with a property which is equivalent to generalised-lushness for separable spaces. It thus may be seemed as geometrical of Banach space ensures the have Mazur–Ulam property. We prove that X enjoys this if and only C(K, X) also show same result holds $$L_\infty (\mu ,X)$$ $$L_1(\mu .

Abstract We prove that every commutative JB $$^*$$ ∗ -triple, represented as a space of continuous functions $$C_0^{\mathbb {T}}(L),$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">C0T<mml:m...

The Topological Radon Theorem states that, for every continuous function from the boundary of a (d + 1)-dimensional simplex into Rn, there exist a pair of disjoint faces in the domain whose images intersect in Rn. The similarity between that result and the classical Borsuk-Ulam Theorem is unmistakeable, but a proof that the Topological Radon Theorem follows from Borsuk-Ulam is not immediate. In...

Let N = (R,+, ·, <, . . . ) be an o-minimal expansion of the standard structure of a real closed field R. A definably compact definable group G is a definable Borsuk-Ulam group if there exists an isovariant definable map f : V → W between representations of G, then dimV − dimV G ≤ dimW − dimW. We prove that if a finite group G satisfies the prime condition, then G is a definable Borsuk-Ulam gro...

We study the Fadell–Husseini index of the configuration space F (R, n) with respect to different subgroups of the symmetric group Sn. For p prime and k ≥ 1, we completely determine IndexZ/p(F (R, p);Fp) and partially describe Index(Z/p)k (F (R, p);Fp). In this process we obtain results of independent interest, including: (1) an extended equivariant Goresky–MacPherson formula, (2) a complete des...