On a Theorem of Rudin and Klee
نویسندگان
چکیده
Proof. Let 11 and V be countable bases for X and Y, respectively, and let 3 have as sub-base the collection of sets {fCC(X, Y) \f(U) C V), with UCM and VCÜ. Then 3 certainly has a countable base. Clearly 3 also makes (/, x)—>/(x) jointly continuous, and hence [l, p. 223] is finer than the compact-open topology. Finally, every subset of C(X, Y) is certainly Lindelöf and separable for the countable-base topology 3, and hence also for any coarser topology.
منابع مشابه
On the Ultramean Construction
We use the ultramean construction to prove linear compactness theorem. We also extend the Rudin-Keisler ordering to maximal probability charges and characterize it by embeddings of power ultrameans.
متن کاملMath 140A Homework 9 (Solutions)
Since the series ∑∞n=1 an and ∑∞n=1 1 n2 both converge, the comparison test (Theorem 3.25(a) in Rudin) implies that ∑∞n=1 an n also converges. Problem 2 (Rudin, Chapter 3 #8). If ∑∞n=1 an converges, and if {bn} is monotonic and bounded, prove that ∑∞n=1 anbn converges. Solution. Let ε > 0 be given. Let A = ∑∞n=1 an, and, for each n ∈ N, let An = ∑n k=1 ak, so that An → A as n → ∞. Since the seq...
متن کاملRemarks on acyclic versions of generalized von Neumann and Nash equilibrium theorems
A fixed-point theorem on compact compositions of acyclic maps on admissible (in the sense of Klee) convex subset of a t.v.s. is applied to obtain a cyclic coincidence theorem for acyclic maps, generalized “onNeumann type intersection theorems, the Nash type equilibrium theorems, and the “onNeumann minimax theorem. Our new results generalize earlier works of Lassonde [l], Simons [2], and Park [3...
متن کاملThe Holt-Klee condition for oriented matroids
Holt and Klee have recently shown that every (generic) LP orientation of the graph of a d-polytope satisfies a directed version of the d-connectivity property, i.e. there are d internally disjoint directed paths from a unique source to a unique sink. We introduce two new classes HK and HK* of oriented matroids (OMs) by enforcing this property and its dual interpretation in terms of line shellin...
متن کاملAutomatic Test Generation for String Manipulation Programs using Symbolic Execution
S ymbolic execution of string manipulation programs is challenging as the constraint solvers do not typically support logic over strings and non-string operations. KLEE[1] is a symbolic execution tool used to generate test cases with high coverage. It uses Simple Theorem Prover (STP) as its constraint solver. STP encodes constraints only as bit-vector logic and solves the constraints. It has no...
متن کامل