Open AccessA function space 𝐶_{𝑝}(𝑋) without a condensation onto a 𝜎-compact space
Author(s) -
Witold Marciszewski
Publication year - 2002
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/s0002-9939-02-06668-6
Subject(s) - algorithm , annotation , computer science , type (biology) , artificial intelligence , database , biology , ecology
Assuming that the minimal cardinality of a dominating family in ω ω \omega ^{\omega } is equal to 2 ω 2^{\omega } , we construct a subset X X of a real line R \mathbb {R} such that the space C p ( X ) C_{p}(X) of continuous real-valued functions on X X does not admit any continuous bijection onto a σ \sigma -compact space. This gives a consistent answer to a question of Arhangel’skii.