# 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

## Access Full Article

top## Abstract

top## How to cite

topMert 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

top- [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. Zbl55.0960.02
- [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 Zbl0473.54015
- [5] R. Engelking: “On the double circumference of Alexandroff”, Bull. Acad. Pol. Sci. Ser. Math., Vol. 16, (1968), pp. 629–634. Zbl0167.21001
- [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] K. Kunen and J.E. Vaughan: Handbook of Set-Theoretic Topology, North-Holland, 1984. Zbl0546.00022
- [8] V. Troitsky: “On CD 0(K)-spaces”, Vladikavkaz. Mat. Zh., Vol. 6(1), (2004), pp. 71–73.

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.