A NOTE ON NON-FRAGMENTABLE SUBSPACE OF \(\ell_ ꝏ^{c}\)(Γ)

Abstract

In this paper we consider \(\ell_ ꝏ^{c}\)(Γ) where Γ is uncountable and introduce subspaces {\(A_\mathcal{P}\)}\(_{\mathcal{P} ∈ Σ}\) of \(\ell_ ꝏ^{c}\)(Γ) which are fragmented by a metric that generates the discrete topology but A = \(\bigcup_{\mathcal{P} ∈ Σ}\) A\(_\mathcal{P}\) is not countable unions of fragmentable subspaces.