Generalized Alexandroff Duplicates and CD 0(K) spaces

Mert Çaglar; Zafer Ercan; Faruk Polat

Open Mathematics (2006)

  • Volume: 4, Issue: 3, page 371-375
  • ISSN: 2391-5455

Abstract

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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].

How to cite

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Mert Çaglar, Zafer Ercan, and Faruk Polat. "Generalized Alexandroff Duplicates and CD 0(K) spaces." Open Mathematics 4.3 (2006): 371-375. <http://eudml.org/doc/269236>.

@article{MertÇaglar2006,
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].},
author = {Mert Çaglar, Zafer Ercan, Faruk Polat},
journal = {Open Mathematics},
keywords = {46D80; 54C35},
language = {eng},
number = {3},
pages = {371-375},
title = {Generalized Alexandroff Duplicates and CD 0(K) spaces},
url = {http://eudml.org/doc/269236},
volume = {4},
year = {2006},
}

TY - JOUR
AU - Mert Çaglar
AU - Zafer Ercan
AU - Faruk Polat
TI - Generalized Alexandroff Duplicates and CD 0(K) spaces
JO - Open Mathematics
PY - 2006
VL - 4
IS - 3
SP - 371
EP - 375
AB - 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].
LA - eng
KW - 46D80; 54C35
UR - http://eudml.org/doc/269236
ER -

References

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  1. [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. [2] P.S. Alexandroff and P.S. Urysohn: Memoire sur les espaces topologiques compacts, Verh. Kon. Akad. Wetensch. Naturkunde. 14, Amsterdam, 1929. Zbl55.0960.02
  3. [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. [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 Zbl0473.54015
  5. [5] R. Engelking: “On the double circumference of Alexandroff”, Bull. Acad. Pol. Sci. Ser. Math., Vol. 16, (1968), pp. 629–634. Zbl0167.21001
  6. [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 Zbl1050.46022
  7. [7] K. Kunen and J.E. Vaughan: Handbook of Set-Theoretic Topology, North-Holland, 1984. Zbl0546.00022
  8. [8] V. Troitsky: “On CD 0(K)-spaces”, Vladikavkaz. Mat. Zh., Vol. 6(1), (2004), pp. 71–73. 

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