Open AccessNuclear and integral polynomials on testing $\mathsf C^{(I)}, \;\; I$ uncountable
Author(s) -
Christopher Boyd
Publication year - 2003
Publication title -
mathematica scandinavica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.553
H-Index - 30
eISSN - 1903-1807
pISSN - 0025-5521
DOI - 10.7146/math.scand.a-14426
Subject(s) - uncountable set , mathematics , homogeneous , class (philosophy) , regular polygon , combinatorics , discrete mathematics , pure mathematics , geometry , countable set , artificial intelligence , computer science
We show that for $I$ an uncountable index set and $n\ge 3$ the spaces of all $n$-homogeneous polynomials, all $n$-homogeneous integral polynomials and all $n$-homogeneous nuclear polynomials are all different. Using this result we then show that the class of locally Asplund spaces is not preserved under uncountable locally convex direct sums nor is separably determined.