The Necessary Condition For Fixed Points In The Inverse Limits Spaces
Main Article Content
Abstract
A point in the inverse limit space is said to be a cut point of this space when excluded from it, when the number of the components of that space increases. Therefore, this study aims at finding the necessary condition for fixed points in the inverse limit space to be cut points. Then, for applying the main theorem with some conditions, a sequence of upper semi continuous can be employed as a bonding function to get a union of continua as a generalized inverse limit space if there is a generalized inverse limit for each of them separately.
Article Details

This work is licensed under a Creative Commons Attribution 4.0 International License.
Tikrit Journal of Pure Science is licensed under the Creative Commons Attribution 4.0 International License, which allows users to copy, create extracts, abstracts, and new works from the article, alter and revise the article, and make commercial use of the article (including reuse and/or resale of the article by commercial entities), provided the user gives appropriate credit (with a link to the formal publication through the relevant DOI), provides a link to the license, indicates if changes were made, and the licensor is not represented as endorsing the use made of the work. The authors hold the copyright for their published work on the Tikrit J. Pure Sci. website, while Tikrit J. Pure Sci. is responsible for appreciate citation of their work, which is released under CC-BY-4.0, enabling the unrestricted use, distribution, and reproduction of an article in any medium, provided that the original work is properly cited.
References
[1] Mahavier W. S. (2004). Inverse limits with subsets of [0,1]×[0,1], Topology and its Applications, 141(1-3), 225–231.
[2] Ingram, T. W. and Mahavier, W. S. (2006). Inverse limits of upper semi-continuous set valued functions, Houston Journal of Mathematics. 32, 119–130.
[3] Banic I. and Martinez, V. (2015). Universal dendrite D3 as a generalized inverse limit. Houston Journal of
Mathematics. 41 (2), 669-682.
[4] Garcia, M. A. C. (2022). Dendrites in generalized inverse limits. Topology and its Applications. 308 (1), 108001.
[5] Marsh, M. M. (2022). Atriodic tree-like continua as inverse limits on [0,1] with interval-valued functions. Topology and its Applications. 308(1), 107997.
[6] Ingram, W. T. (2012). An Introduction to Inverse Limits with Set-valued Functions. Springer, New York.
[7] Ingram, W. T. and Mahavier, W. S. (2012). Inverse Limits: from continua to chaos (Vol. 25), Developments in Mathematics, vol. 25. Springer, New York
[8] Macias, S. (2005). Topics on Continua. Boca Raton: Chapman & Hall/CRC.
[9] Sam B. Nadler Jr., (1978). Hyperspaces of sets. Monographs and Textbooks in Pure applied mathematics (Vol. 49), Marcel Dekker, Inc. New York.
[10] Sam B. Nadler Jr., (1992). Continuum theory. Monographs and Textbooks in Pure and Applied Mathematics, (Vol. 158), Marcel Dekker, Inc. New York.
[11] Kuratowski, K. (1968). Topology. volume II, Academic Press, New York, London and Warszawa.
[12] Abul-jabbar, R. S. (2019). On fixed point theorem in complete quasi-metric space under F-contraction mapping. Tikrit Journal of Pure Science. 24(2). 88-90
[13] Arévalo, D., Charatonik, W. J., Covarrubias, P. P., and Simón, L. (2001). Dendrites with a closed set of end points. Topology and its Applications, 115(1), 1-17.
[14] Willard, Stephen. (1970). General Topology. Courier Corporation, Addison-Wesley Inc.
[15] Imamura, H. (2019). Markov-like set-valued functions on finite graphs and their inverse limits, Topology and its Applications. 264, 175–186.