1964/08/01 by R. Seeley · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Numerical methods in inverse problems #Functional Equations Stability Results #Extension (predicate logic) #Mathematics #Closure (psychology) #Boundary (topology) #Connection (principal bundle) #Space (punctuation) #Topology (electrical circuits) #Function (biology) #Function space #Continuous function (set theory) #Pure mathematics #Mathematical analysis #Transformation (genetics) #Combinatorics #Geometry #Computer science
paper · pdf · doi:10.1090/s0002-9939-1964-0165392-8
openalex publication_date 1964/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/05/06
The following question arises in connection with manifolds with boundary: given a function f defined and Co in a half space, and all of whose derivatives have continuous limits at the boundary, can f be extended to a Coo function in the whole space? More specifically, let xERn, tER, S+ = Rn X t > 0 , and D+ = f: f in CW?(S+), f and all its derivatives have continuous limits as t-0 .+ . D+ has the topology of uniform convergence of each derivative on compact subsets of the closure of S+ in Rn+l, and C??(Rn+l) has a corresponding topology.