Note on function spaces with the topology of pointwise convergence
نویسندگان
چکیده
منابع مشابه
Note on function spaces with the topology of pointwise convergence
The note contains two examples of function spaces Cp(X) endowed with the pointwise topology. The first example is Cp(M),M being a planar continuum, such that Cp(M) is uniformly homeomorphic to Cp(M) if and only ifm = n. This strengthens earlier results concerning linear homeomorphisms. The second example is a non-Lindelöf function space Cp(X), whereX is a monolithic perfectly normal compact spa...
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Let G be a topological group with the identity element e. Given a space X, we denote by Cp(X,G) the group of all continuous functions from X to G endowed with the topology of pointwise convergence, and we say that X is: (a) G-regular if, for each closed set F ⊆ X and every point x ∈ X \ F , there exist f ∈ Cp(X,G) and g ∈ G \ {e} such that f(x) = g and f(F ) ⊆ {e}; (b) G-regular provided that t...
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ژورنال
عنوان ژورنال: Archiv der Mathematik
سال: 2003
ISSN: 0003-889X,1420-8938
DOI: 10.1007/s00013-003-0032-9