The Kuratowski-Mrówka characterization and weak forms of compactness

Published

2009-01-01

The Kuratowski-Mrówka characterization and weak forms of compactness

La caracterización de Kuratowski-Mrówka y formas débiles de compacidad

Keywords:

Kuratowski-Mrówka characterization of compact spaces, closure operator, weak form of compactness (en)
Caracterización de Kuratowski-Mrówka de los espacios compactos, operador de clausura, formas débiles de compacidad (es)

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Universidad Nacional de Colombia, Bogotá, Colombia

Abstract (en)
Abstract (es)

Abstract. For cardinals κ > ℵ_o, characterizations of the Kuratowski-Mrówka type of initial κ-compactness and final κ-compactness are given. Moreover, a categorical characterization of κ-compactness is given in terms of a closure operator depending on an ultrafilter over κ.

Se presentan caracterizaciones del tipo Kuratowski-Mrówka de la κ-compacidad inicial y de la κ-compacidad final, donde κ > ℵ_o es un cardinal. Además, se presenta una caracterización categórica de la κ-compacidad, en términos de un operador de clausura que depende de un ultrafiltro sobre κ.

References

N. Bourbaki, General topology, Addison Wesley, New York, 1966.

X. Caicedo, El teorema de Tychonoff para formas débiles de compacidad, Boletín de Matemáticas V (1998), no. 1, 1-13 (es).

M. M. Clementino, On categorical notions of compact objects, Applied Categorical Structures 4 (1996), 15-29.

M. M. Clementino, E. Giuli, and W. Tliolen, Topology in a category: Compactness, Portugaliae Mathematica 53 (1996), no. 4, 397-433.

H. Herrlich, G. Salicrup, and G. E. Strecker, Factorizations, denseness, separation and relatively compact objects, Topology Appi. 27 (1987), 157-169.

H. J. Keisler, On cardinalities of ultraproducts, Bull. Amer. Math. Soc. 7 0 (1964), 644-647.

E. G. Manes, Compact Hausdorff objects, Gen. Topology Appi. 4 (1974), 341-360.

How to Cite

APA

Clara M. (2009). The Kuratowski-Mrówka characterization and weak forms of compactness. Revista Colombiana de Matemáticas, 43(1), 9–17. https://revistas.unal.edu.co/index.php/recolma/article/view/95511

ACM

[1]

Clara M. 2009. The Kuratowski-Mrówka characterization and weak forms of compactness. Revista Colombiana de Matemáticas. 43, 1 (Jan. 2009), 9–17.

ACS

(1)

Clara M. The Kuratowski-Mrówka characterization and weak forms of compactness. rev.colomb.mat 2009, 43, 9-17.

ABNT

CLARA M. The Kuratowski-Mrówka characterization and weak forms of compactness. Revista Colombiana de Matemáticas, [S. l.], v. 43, n. 1, p. 9–17, 2009. Disponível em: https://revistas.unal.edu.co/index.php/recolma/article/view/95511. Acesso em: 22 jan. 2025.

Chicago

Clara M. 2009. “The Kuratowski-Mrówka characterization and weak forms of compactness”. Revista Colombiana De Matemáticas 43 (1):9-17. https://revistas.unal.edu.co/index.php/recolma/article/view/95511.

Harvard

Clara M. (2009) “The Kuratowski-Mrówka characterization and weak forms of compactness”, Revista Colombiana de Matemáticas, 43(1), pp. 9–17. Available at: https://revistas.unal.edu.co/index.php/recolma/article/view/95511 (Accessed: 22 January 2025).

IEEE

[1]

Clara M., “The Kuratowski-Mrówka characterization and weak forms of compactness”, rev.colomb.mat, vol. 43, no. 1, pp. 9–17, Jan. 2009.

MLA

Clara M. “The Kuratowski-Mrówka characterization and weak forms of compactness”. Revista Colombiana de Matemáticas, vol. 43, no. 1, Jan. 2009, pp. 9-17, https://revistas.unal.edu.co/index.php/recolma/article/view/95511.

Turabian

Clara M. “The Kuratowski-Mrówka characterization and weak forms of compactness”. Revista Colombiana de Matemáticas 43, no. 1 (January 1, 2009): 9–17. Accessed January 22, 2025. https://revistas.unal.edu.co/index.php/recolma/article/view/95511.

Vancouver

1.

Clara M. The Kuratowski-Mrówka characterization and weak forms of compactness. rev.colomb.mat [Internet]. 2009 Jan. 1 [cited 2025 Jan. 22];43(1):9-17. Available from: https://revistas.unal.edu.co/index.php/recolma/article/view/95511