Öz
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.
Anahtar Kelimeler
Distance lower regular function frame approach structure approach space contraction Vietoris topology Fell topology index of compactness
Kaynakça
- 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
Öz
Kaynakça
- 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
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Research Article |
| Yazarlar | |
| Yayımlanma Tarihi | 30 Eylül 2023 |
| Gönderilme Tarihi | 26 Aralık 2022 |
| Kabul Tarihi | 28 Mart 2023 |
| Yayımlandığı Sayı | Yıl 2023 |
Kaynak Göster
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.
