DOI: 10.2478/s11533-006-0018-5 Research article CEJM 4(3) 2006 371–375 Generalized Alexandroff Duplicates and CD 0 (K ) spaces Mert ¸ Caglar ∗ , Zafer Ercan, Faruk Polat MiddleEast Technical University, Department of Mathematics, 06531 Ankara, Turkey Received 26 October 2005; accepted 15 April 2006 Abstract: We define and investigateCD Σ,Γ (K, E)-type spaces, which generalizeCD 0 -type Banach lattices introduced in [1]. We state that the space CD Σ,Γ (K, E) can be represented as the space of E-valued continuous functions on the generalized Alexandroff Duplicate of K. As a corollary we obtain the main result of [6, 8]. c  Versita Warsaw and Springer-Verlag Berlin Heidelberg. All rights reserved. Keywords: Alexandroff Duplicate, homeomorphism, Banach lattices, CD 0 (K, E)-spaces MSC (2000): 46D80, 54C35 1 Introduction Throughout this paper E denotes a Banach lattice and Ω, Σ and Γ stand for topologies on K , where Σ is compact Hausdorff space,Γ is a locally compact Hausdorff space with Σ ⊂ Γ. These spaces are denoted by K Ω , K Σ and K Γ . The closure of a subset A of K Ω is denoted by cl Ω (A). As usual, the space of E-valued K Ω -continuous functions on K is denoted by C (K Ω ,E), or by C (K, E) if there is no possibility of confusion. C 0 (K Γ ,E) denotes the space of E-valued K Γ -continuous functions d on K such that for each ǫ> 0 there exists a compact set M with ||d(k)|| ≤ ǫ for each k ∈ K \ M . We write C (K Ω , R)= C (K Ω ) and C 0 (K Γ , R)= C 0 (K Γ ). If K Σ has no isolated points and K Γ is discrete then C (K Σ ,E) ∩ C 0 (K Γ ,E)= {0}, and CD 0 (K Σ ,E)= C (K Σ ,E) ⊕ C 0 (K Γ ,E) is a Banach lattice under point wise order and supremum norm. We refer to [1, 3] and [6] for more detail on these spaces. CD Σ,Γ (K, E) denotes the vector space C (K Σ ,E) × * E-mail:zercan@metu.edu.tr