Abstract
In the present paper we construct a new approach structure called Fell approach structure. We define the new structure by means of lower regular function frames and prove that the Top-coreflection of this new structure is the ordinary Fell topology. We also give analogue result for the extended Fell topology and investigate some properties of Fell approach structure.
Keywords
Distance lower regular function frame approach structure approach space contraction Vietoris topology Fell topology index of compactness
References
- Beer, G., Kenderov, P. On the arg min multifunction for lower semicontinuous functions, Proc. Amer. Math. Soc., 102 (1988), 107-113. https://doi.org/10.1090/S0002-9939-1988-0915725-3
- Beer, G., Luchetti, R., Convex optimization and epi-distance topology, Trans. Amer. Math. Soc., 327 (1991), 795-813. https://doi.org/10.2307/2001823
- Beer, G., On the Fell topology, Set Valued Analysis, 1 (1993), 69-80. https://doi.org/10.1007/BF01039292
- Beer, G., Topologies on Closed Convex Sets, Kluwer Academic Publishers, 1993. http://dx.doi.org/10.1007/978-94-015-8149-3
- Fell, J., A Hausdorff topology for the closed subsets of locally compact non-Hausdorff space, Proc. Amer. Math. Soc., 13 (1962), 472-476. https://doi.org/10.1090/S0002-9939-1962-0139135-6
- Hola, L., Levi, S., Decomposition properties of hyperspace topologies, Set Valued Analysis, Kluwer Academic Publishers (1997). https://doi.org/10.1023/A:1008608209952
- Baran, M., Qasim, M., Local $T_{0}$ approach spaces, Mathematical Sciences and Applications E-Notes, 5(1) (2017), 45-56.
- Baran, M., Qasim, M., $T_{1}$ approach spaces, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(1) (2019), 784-800. https://doi.org/10.31801/cfsuasmas.478632
- Bourbaki, N., Theory of Sets, Elements of Mathematics, Springer, Heidelberg, 2004.
- Lowen, R. Kuratowski’s measure of noncompactness revisited, Q.J. Math. Oxford, 39 (1988), 235-254. https://doi.org/10.1093/qmath/39.2.235
- Lowen, R., Sioen, M., The Wijsman and Attouch-Wets topologies on hyperspaces revisited, Topology Appl., 70 (1996), 179-197. https://doi.org/10.1016/0166-8641(95)00096-8
- Lowen, R., Approach Spaces: the Missing Link in the Topology Uniformity Metric Triad, Oxford Mathematical Monographs. Oxford University Press, New York, United States Springer, 1997.
- Lowen, R., Verbeeck, C., Local compactness in approach spaces I, Internat. J. Math. Scie., 21 (1998), 429-438. https://doi.org/10.1155/S0161171203007646
- Lowen, R., Sioen, M., Proximal hypertopologies revisited, Set Valued Analysis, 6 (1998), 1-19. http://dx.doi.org/10.1023/A:1008646106442
- Lowen, R., Sioen, M., A note on seperation in Ap, Applied General Topology, 4 (2003), 475-486. http://dx.doi.org/10.4995/agt.2003.2046
- Lowen, R., Wuyts, P., The Vietoris hyperspace structure for approach spaces, Acta Math. Hungar., 139, (2013), 286–302. http://dx.doi.org/10.1007/s10474-012-0292-6
- Lowen, R. Index Analysis, Approach Theory at Work, Springer, 2015. http://dx.doi.org/10.1007/978-1-4471-6485-2
Abstract
References
- Beer, G., Kenderov, P. On the arg min multifunction for lower semicontinuous functions, Proc. Amer. Math. Soc., 102 (1988), 107-113. https://doi.org/10.1090/S0002-9939-1988-0915725-3
- Beer, G., Luchetti, R., Convex optimization and epi-distance topology, Trans. Amer. Math. Soc., 327 (1991), 795-813. https://doi.org/10.2307/2001823
- Beer, G., On the Fell topology, Set Valued Analysis, 1 (1993), 69-80. https://doi.org/10.1007/BF01039292
- Beer, G., Topologies on Closed Convex Sets, Kluwer Academic Publishers, 1993. http://dx.doi.org/10.1007/978-94-015-8149-3
- Fell, J., A Hausdorff topology for the closed subsets of locally compact non-Hausdorff space, Proc. Amer. Math. Soc., 13 (1962), 472-476. https://doi.org/10.1090/S0002-9939-1962-0139135-6
- Hola, L., Levi, S., Decomposition properties of hyperspace topologies, Set Valued Analysis, Kluwer Academic Publishers (1997). https://doi.org/10.1023/A:1008608209952
- Baran, M., Qasim, M., Local $T_{0}$ approach spaces, Mathematical Sciences and Applications E-Notes, 5(1) (2017), 45-56.
- Baran, M., Qasim, M., $T_{1}$ approach spaces, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(1) (2019), 784-800. https://doi.org/10.31801/cfsuasmas.478632
- Bourbaki, N., Theory of Sets, Elements of Mathematics, Springer, Heidelberg, 2004.
- Lowen, R. Kuratowski’s measure of noncompactness revisited, Q.J. Math. Oxford, 39 (1988), 235-254. https://doi.org/10.1093/qmath/39.2.235
- Lowen, R., Sioen, M., The Wijsman and Attouch-Wets topologies on hyperspaces revisited, Topology Appl., 70 (1996), 179-197. https://doi.org/10.1016/0166-8641(95)00096-8
- Lowen, R., Approach Spaces: the Missing Link in the Topology Uniformity Metric Triad, Oxford Mathematical Monographs. Oxford University Press, New York, United States Springer, 1997.
- Lowen, R., Verbeeck, C., Local compactness in approach spaces I, Internat. J. Math. Scie., 21 (1998), 429-438. https://doi.org/10.1155/S0161171203007646
- Lowen, R., Sioen, M., Proximal hypertopologies revisited, Set Valued Analysis, 6 (1998), 1-19. http://dx.doi.org/10.1023/A:1008646106442
- Lowen, R., Sioen, M., A note on seperation in Ap, Applied General Topology, 4 (2003), 475-486. http://dx.doi.org/10.4995/agt.2003.2046
- Lowen, R., Wuyts, P., The Vietoris hyperspace structure for approach spaces, Acta Math. Hungar., 139, (2013), 286–302. http://dx.doi.org/10.1007/s10474-012-0292-6
- Lowen, R. Index Analysis, Approach Theory at Work, Springer, 2015. http://dx.doi.org/10.1007/978-1-4471-6485-2
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Research Articles |
| Authors | |
| Publication Date | September 30, 2023 |
| Submission Date | December 26, 2022 |
| Acceptance Date | March 28, 2023 |
| Published in Issue | Year 2023 Volume: 72 Issue: 3 |
Cite
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.
