Generalized Alexandroff Duplicates and CD 0(K) spaces

• Autorzy: Mert Çaglar , Zafer Ercan , Faruk Polat
• Języki publikacji: EN

Abstrakty

EN

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].

Słowa kluczowe

EN

Alexandroff Duplicate; homeomorphism; Banach lattices; CD0(K, E)-spaces; 46D80; 54C35

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2006
• Tom: 4
• Numer: 3
• Strony: 371-375

Daty

wydano

2006-09-01

online

2006-09-01

Twórcy

autor

Mert Çaglar

• MiddleEast Technical University

autor

Zafer Ercan

• MiddleEast Technical University

autor

Faruk Polat

• MiddleEast Technical University

Bibliografia

• [1] Y. Abramovich and A.W. Wickstead: “Remarkable classes ofunitial AM-spaces”, J. Math. Anal. Appl., Vol. 180, (1993), pp, 398–411. http://dx.doi.org/10.1006/jmaa.1993.1408
• [2] P.S. Alexandroff and P.S. Urysohn: Memoire sur les espaces topologiques compacts, Verh. Kon. Akad. Wetensch. Naturkunde. 14, Amsterdam, 1929.
• [3] S. Alpay and Z. Ercan: “CD 0(K, E) and CD w (K, E) spaces asBanach lattices”, Positivity, Vol. 3, (2000), pp. 213–225. http://dx.doi.org/10.1023/A:1009878527795
• [4] R.E. Chandler, G.D. Faulkner, J.P. Guglielmi and M.C. Memory: “Generalizing the Alexandroff-Urysohn double circumference construction”, Proc. Amer. Math. Soc., Vol. 83(3), (1981), pp. 606–608. http://dx.doi.org/10.2307/2044130
• [5] R. Engelking: “On the double circumference of Alexandroff”, Bull. Acad. Pol. Sci. Ser. Math., Vol. 16, (1968), pp. 629–634.
• [6] Z. Ercan: “A concrete description of CD 0(K)-spaces as C(X)-spaces and its applications”, Proc. Amer. Math. Soc., Vol. 132(6), (2004), pp. 1761–1763. http://dx.doi.org/10.1090/S0002-9939-03-07235-6
• [7] K. Kunen and J.E. Vaughan: Handbook of Set-Theoretic Topology, North-Holland, 1984.
• [8] V. Troitsky: “On CD 0(K)-spaces”, Vladikavkaz. Mat. Zh., Vol. 6(1), (2004), pp. 71–73.

Identyfikatory

DOI

10.2478/s11533-006-0018-5