Abstract
We gather some of the results of topology of metric spaces which will be useful for the rest of the book. We assume the reader is familiar with the notion of metric space and its elementary properties. We present the proofs of most of the results; we give an appropriate reference otherwise.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
M. Aguilar, S. Gitler and C. Prieto, Algebraic Topology From a Homotopical Viewpoint, Universitext, Springer-Verlag, New York, Inc., 2002.
F. D. Ancel, An Alternative Proof and Applications of a Theorem of E. G. Effros, Michigan J. 34 (1987), 39–55.
D. P. Bellamy, The cone over the Cantor set-continuous maps from both directions, in: Proceedings of the Topology Conference, J. W. Rogers, Jr., ed., Emory University, Atlanta GA, (1970), 8–25.
K. Borsuk and S. Ulam, On Symmetric Products of Topological Spaces, Bull. Amer. Math. Soc., 37 (1931), 875–882.
E. Castañeda, A Unicoherent Continuum for Which its Second Symmetric Product is not Unicoherent, Topology Proceedings, 23 (1998), 61–67.
E. Castañeda, Productos Simétricos, Tesis Doctoral, Facultad de Ciencias, U. N. A. M., 2003. (Spanish)
J. J. Charatonik, On fans, Dissertationes Math. (Rozprawy Mat.), 54 (1967), 1–37.
J. J. Charatonik, A. Illanes and S. Macías, Induced Mappings on the Hyperspaces \(\mathcal {C}_n(X)\) of a Continuum X, Houston J. Math., 28 (2002), 781–805.
H. S. Davis, P. H. Doyle, Invertible Continua, Portugal. Math., 26 (1967), 487–491.
J. Dugundji, Topology, Allyn and Bacon, Inc., Boston, 1966.
J. B. Fugate, G. R. Gordh, Jr. and L. Lum, Arc-smooth Continua, Trans. Amer. Math. Soc., 265 (1981), 545–561.
G. R. Gordh, Jr. and C. B. Hughes, On Freely Decomposable Mappings of Continua, Glasnik Math., 14 (34) (1979), 137–146.
J. G. Hocking and G. S. Young, Topology, Dover Publications, Inc., New York, 1988.
F. B. Jones, Aposyndetic Continua and Certain Boundary Problems, Amer. J. Math., 53 (1941), 545–553.
A. Illanes and S. B. Nadler, Jr., Hyperspaces: Fundamentals and Recent Advances, Monographs and Textbooks in Pure and Applied Math., Vol. 216, Marcel Dekker, New York, Basel, 1999.
K. Kuratowski, Topology, Vol. I, Academic Press, New York, N. Y., 1966.
K. Kuratowski, Topology, Vol. II, Academic Press, New York, N. Y., 1968.
E. L. Lima, Espaços Métricos, terceira edição, Instituto de Matemática Pura e Aplicada, CNPq, (Projeto Euclides), 1977. (Portuguese)
E. L. Lima, Grupo Fundamental e Espaços de Recobrimento, Instituto de Matemática Pura e Aplicada, CNPq, (Projeto Euclides), 1993. (Portuguese)
S. Macías, On Symmetric Products of Continua, Topology Appl., 92 (1999), 173–182.
S. Macías, Aposyndetic Properties of Symmetric Products of Continua, Topology Proc., 22 (1997), 281–296.
S. Macías, On the Hyperspaces \(\mathcal {C}_n(X)\) of a Continuum X, Topology Appl., 109 (2001), 237–256.
S. Macías, On the Hyperspaces \(\mathcal {C}_n(X)\) of a Continuum X, II, Topology Proc., 25 (2000), 255–276.
J. Munkres, Elements of Algebraic Topology, Addison-Wesley Publishing Company, Inc., Redwood City, California, 1984.
J. Munkres, Topology, second edition, Prentice Hall, Upper Saddle River, NJ, 2000.
S. B. Nadler, Jr., 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.
S. B. Nadler, Jr., Continuum Theory: An Introduction, Monographs and Textbooks in Pure and Applied Math., Vol. 158, Marcel Dekker, New York, Basel, Hong Kong, 1992.
S. B. Nadler, Jr., Continuum Theory, class notes, Fall Semester of 1999, Math. 481, West Virginia University.
J. J. Rotman, An Introduction to the Theory of Groups, fourth edition, Graduate Texts in Mathematics, Vol. 148, Springer-Verlag, New York, Inc., 1995.
W. Rudin, Principles of Mathematical Analysis, third edition, International Series in Pure and Applied Mathematics, McGraw-Hill, Inc., New York, 1976.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Macías, S. (2018). Preliminaries. In: Topics on Continua. Springer, Cham. https://doi.org/10.1007/978-3-319-90902-8_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-90902-8_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-90901-1
Online ISBN: 978-3-319-90902-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)