Research and Innovation Articles
Published 2019-02-19
Keywords
- Atomic map,
- Effros continuum,
- homogeneous continuum,
- property of Kelley,
- set function T
- uniform property of Effros ...More
How to Cite
Macías, S. (2019). The property of Kelley and continua. Revista Integración, Temas De matemáticas, 37(1), 17–29. https://doi.org/10.18273/revint.v37n1-2019002
Abstract
We study Hausdorff continua with the property of Kelley. We present Hausdorff version of several results known in the metric case. We also establish a weak Hausdorff version of Jones’ Aposyndetic Decomposition Theorem.
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References
[1] Bellamy D.P. and Lum L., “The Cyclic Connectivity of Homogeneous Arcwise Connected Continua”, Trans. Amer. Math. Soc. 266 (1981), 389–396.
[2] Camargo J., Macías S. and Uzcátegui C., “On the images of Jones’ set function T ”, Colloq. Math. 153 (2018), 1–19.
[3] Charatonik W.J., “A homogeneous continuum without the property of Kelley”, Topology Appl. 96 (1999), 209–216.
[4] Christenson C. and Voxman W., Aspects of Topology, Monographs and Textbooks in Pure and Applied Math., Vol. 39, Marcel Dekker, New York, Basel, 1977.
[5] Engelking R., General Topology, Sigma series in pure mathematics, Vol. 6, Heldermann, Berlin, 1989.
[6] Hocking J. and Young G., Topology, Dover, 1988.
[7] Kelley J.L., “Hyprespaces of a continuum”, Trans. Amer. Math. Soc. 52 (1942), 22–36.
[8] Macías S., Topics on Continua, 2nd edition, Springer, 2018.
[9] Macías S., “A Decomposition Theorem for a Class of Continua for Which the Set Function T is Continuous”, Colloq. Math. 109 (2007), 163–170.
[10] Macías S., “On the Idempotency of the Set Function T ”, Houston J. Math. 37 (2011), 1297–1305.
[11] Macías S., “On Jones’ set function T and the property of Kelley for Hausdorff continua”, Topology Appl. 226 (2017), 51–65.
[12] Macías S., “Hausdorff continua and the uniform property of Effros”, Topology Appl. 230 (2017), 338–352.
[13] Macías S. and Nadler Jr. S.B., “Various types of local connectedness in n-fold hyperspaces”, Topology Appl. 154 (2007), 39–53.
[14] Makuchowski W., “On local connectedness in hyperspaces”, Bull. Pol. Acad. Sci. 47 (1999), 119–126.
[15] Michael E., “Topologies on spaces of subsets”, Trans. Amer. Math. Soc. 71 (1951), 152–182.
[16] Misra A.K., “C-supersets, piecewise order-arcs and local arcwise connectedness in hyperspaces”, Q. & A. in General Topology, 8 (1990), 467–485.
[17] Mrówka S., “On the convergence of nets of sets”, Fund. Math. 45 (1958), 237–246.
[18] Nadler Jr. S.B., Hyperspaces of Sets, Monographs and Textbooks in Pure and Applied Math., Vol. 49, Marcel Dekker, New York, Basel, 1978. Reprinted in: Aportaciones Matemáticas de la Sociedad Matemática Mexicana, Serie Textos # 33, 2006.
[19] Wardle R.W., “On a property of J. L. Kelley”, Houston J. Math. 3 (1977), 291–299.
[20] Wojdysławski M., “Sur la contractibilité des hyperspaces des continus localment connexes”, Fund. Math. 30 (1938), 247–252.
[2] Camargo J., Macías S. and Uzcátegui C., “On the images of Jones’ set function T ”, Colloq. Math. 153 (2018), 1–19.
[3] Charatonik W.J., “A homogeneous continuum without the property of Kelley”, Topology Appl. 96 (1999), 209–216.
[4] Christenson C. and Voxman W., Aspects of Topology, Monographs and Textbooks in Pure and Applied Math., Vol. 39, Marcel Dekker, New York, Basel, 1977.
[5] Engelking R., General Topology, Sigma series in pure mathematics, Vol. 6, Heldermann, Berlin, 1989.
[6] Hocking J. and Young G., Topology, Dover, 1988.
[7] Kelley J.L., “Hyprespaces of a continuum”, Trans. Amer. Math. Soc. 52 (1942), 22–36.
[8] Macías S., Topics on Continua, 2nd edition, Springer, 2018.
[9] Macías S., “A Decomposition Theorem for a Class of Continua for Which the Set Function T is Continuous”, Colloq. Math. 109 (2007), 163–170.
[10] Macías S., “On the Idempotency of the Set Function T ”, Houston J. Math. 37 (2011), 1297–1305.
[11] Macías S., “On Jones’ set function T and the property of Kelley for Hausdorff continua”, Topology Appl. 226 (2017), 51–65.
[12] Macías S., “Hausdorff continua and the uniform property of Effros”, Topology Appl. 230 (2017), 338–352.
[13] Macías S. and Nadler Jr. S.B., “Various types of local connectedness in n-fold hyperspaces”, Topology Appl. 154 (2007), 39–53.
[14] Makuchowski W., “On local connectedness in hyperspaces”, Bull. Pol. Acad. Sci. 47 (1999), 119–126.
[15] Michael E., “Topologies on spaces of subsets”, Trans. Amer. Math. Soc. 71 (1951), 152–182.
[16] Misra A.K., “C-supersets, piecewise order-arcs and local arcwise connectedness in hyperspaces”, Q. & A. in General Topology, 8 (1990), 467–485.
[17] Mrówka S., “On the convergence of nets of sets”, Fund. Math. 45 (1958), 237–246.
[18] Nadler Jr. S.B., Hyperspaces of Sets, Monographs and Textbooks in Pure and Applied Math., Vol. 49, Marcel Dekker, New York, Basel, 1978. Reprinted in: Aportaciones Matemáticas de la Sociedad Matemática Mexicana, Serie Textos # 33, 2006.
[19] Wardle R.W., “On a property of J. L. Kelley”, Houston J. Math. 3 (1977), 291–299.
[20] Wojdysławski M., “Sur la contractibilité des hyperspaces des continus localment connexes”, Fund. Math. 30 (1938), 247–252.