کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4661229 1344416 2007 10 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Automatic continuity and representation of group homomorphisms defined between groups of continuous functions
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات هندسه و توپولوژی
پیش نمایش صفحه اول مقاله
Automatic continuity and representation of group homomorphisms defined between groups of continuous functions
چکیده انگلیسی

Let C(X,G) be the group of continuous functions from a topological space X into a topological group G with pointwise multiplication as the composition law, endowed with the uniform convergence topology. To what extent does the group structure of C(X,G) determine the topology of X? More generally, when does the existence of a group homomorphism H between the groups C(X,G) and C(Y,G) implies that there is a continuous map h of Y into X such that H is canonically represented by h? We prove that, for any topological group G and compact spaces X and Y, every non-vanishing C-isomorphism (defined below) H of C(X,G) into C(Y,G) is automatically continuous and can be canonically represented by a continuous map h of Y into X. Some applications to specific groups and examples are given in the paper.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 154, Issue 10, 15 May 2007, Pages 2089-2098