- -

Good coverings of proximal Alexandrov spaces. Path cycles in the extension of the Mitsuishi-Yamaguchi good covering and Jordan Curve Theorems

RiuNet: Repositorio Institucional de la Universidad Politécnica de Valencia

Compartir/Enviar a

Citas

Estadísticas

  • Estadisticas de Uso

Good coverings of proximal Alexandrov spaces. Path cycles in the extension of the Mitsuishi-Yamaguchi good covering and Jordan Curve Theorems

Mostrar el registro completo del ítem

Peters, JF.; Vergili, T. (2023). Good coverings of proximal Alexandrov spaces. Path cycles in the extension of the Mitsuishi-Yamaguchi good covering and Jordan Curve Theorems. Applied General Topology. 24(1):25-45. https://doi.org/10.4995/agt.2023.17046

Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/192968

Ficheros en el ítem

Metadatos del ítem

Título: Good coverings of proximal Alexandrov spaces. Path cycles in the extension of the Mitsuishi-Yamaguchi good covering and Jordan Curve Theorems
Autor: Peters, James Francis Vergili, Tane
Fecha difusión:
Resumen:
[EN] This paper introduces proximal path cycles, which lead to the main results in this paper, namely, extensions of the Mitsuishi-Yamaguchi Good Coverning Theorem with different forms of Tanaka good cover of an Alexandrov ...[+]
Palabras clave: Cycle , Good cover , Homotopy , Nerve , Path , Proximity
Derechos de uso: Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)
Fuente:
Applied General Topology. (issn: 1576-9402 ) (eissn: 1989-4147 )
DOI: 10.4995/agt.2023.17046
Editorial:
Universitat Politècnica de València
Versión del editor: https://doi.org/10.4995/agt.2023.17046
Código del Proyecto:
info:eu-repo/grantAgreement/TUBITAK//2221-1059B211301223
info:eu-repo/grantAgreement/NSERC//185986
info:eu-repo/grantAgreement/GNSAGA//9 920160 000362
Agradecimientos:
The first author has been supported by the Natural Sciences & Engineering Research Council of Canada (NSERC) discovery grant 185986 and Instituto Nazionale di Alta Matematica (INdAM) Francesco Severi, Gruppo Nazionale per ...[+]
Tipo: Artículo

References

A. Di Concilio, C. Guadagni, J. F. Peters, and S. Ramanna, Descriptive proximities I: properties and interplay between classical proximities and overlap, Math. Comput. Sci. 12, no. 1 (2018), 91-106. https://doi.org/10.1007/s11786-017-0328-y

V. A. Efremovič, The geometry of proximity {I} (in {R}ussian), Mat. Sb. (N.S.) 31(73), no. 1 (1952), 189-200.

F. Hausdorff, Grundzüge der Mengenlehre, Veit and Company, Leipzig, viii + 476 pp, 1914. [+]
A. Di Concilio, C. Guadagni, J. F. Peters, and S. Ramanna, Descriptive proximities I: properties and interplay between classical proximities and overlap, Math. Comput. Sci. 12, no. 1 (2018), 91-106. https://doi.org/10.1007/s11786-017-0328-y

V. A. Efremovič, The geometry of proximity {I} (in {R}ussian), Mat. Sb. (N.S.) 31(73), no. 1 (1952), 189-200.

F. Hausdorff, Grundzüge der Mengenlehre, Veit and Company, Leipzig, viii + 476 pp, 1914.

F. Hausdorff, Set Theory, trans. by J. R. Aumann, Providence, RI, AMS Chelsea Publishing, 352 pp, 1957.

P. J. Hilton, An introduction to homotopy theory. Cambridge Tracts in Mathematics and Mathematical Physics, no. 43, Cambridge University Press, Cambridge, UK, viii+142 pp, 1953.

C. Jordan, Cours d'analyse de l'École polytechnique, Tome I-III, Éditions Jacques Gabay, Sceaux, 1991 (reprint of 1915 edition, Tome I: MR1188186,Tome II: MR1188187, Tome III: MR1188188).

A. Mitsuishi and T. Yamaguchi, Good coverings of Alexandrov spaces, Trans. Amer. Math. Soc. 372, no. 11 (2019), 8107-8130. https://doi.org/10.1090/tran/7849

L. Mosher, Tiling the projective foliation space of a punctured surface, Trans. Amer. Math. Soc. 306, no.1 (1988), 1-70. https://doi.org/10.1090/S0002-9947-1988-0927683-0

J. R. Munkres, Elements of Algebraic Topology, 2nd Ed., Perseus Publishing, Cambridge, MA, ix + 484 pp, 1984.

S. A. Naimpally and B. D. Warrack, Proximity Spaces, Cambridge Tract in Mathematics No. 59, Cambridge University Press, Cambridge Uk, x+128 pp, 1970.

S. A. Naimpally and J. F. Peters, Preservation of continuity, Scientiae Mathematicae Japonicae 76, no.2 (2013), 305-311.

S. A. Naimpally and J. F. Peters, Topology with Applications. Topological Spaces via Near and Far, World Scientific, Singapore, 2013. https://doi.org/10.1142/8501

J. F. Peters and S. A. Naimpally, Applications of near sets, Notices of the Amer. Math. Soc. 59, no.4 (2012), 536-542. https://doi.org/10.1090/noti817

J. F. Peters, Near sets: An introduction, Math. in Comp. Sci. 7, no. 1 (2013), 3-9. https://doi.org/10.1007/s11786-013-0149-6

J. F. Peters, Topology of Digital Images. Visual Pattern Discovery in Proximity Spaces, Intelligent Systems Reference Library 63, Springer, xv + 411pp, 2014. https://doi.org/10.1007/978-3-642-53845-2

J. F. Peters, Computational Proximity. Excursions in the Topology of Digital Images, Intelligent Systems Reference Library vol.102, Springer, xxviii + 433 pp, 2016.

J. F. Peters, Vortex nerves and their proximities. Nerve Betti numbers and descriptive proximity, Bull. Allahabad Math. Soc. 34, no. 2 (2019), 263-276.

J. F. Peters, Homotopic Nerve Complexes with Free Group Presentations, Int. Online Conf. Alegebraic and Geometric Methods of Analysis, 25-28 May 2021, Odesa, Ukraine, Institute of Mathematics of the National Academy of Sciences of Ukraine,Taras Shevchenko National University of Kyiv, Kyiv Mathematical Society, dedicated to the memory of Yuriy Trokhymchuk, 110-111.

J. F. Peters, E. Inan, A. Tozzi, and S. Ramanna, Bold-Independent Computational Entropy Assesses Functional Donut-Like Structures in Brain fMRI Images, Frontiers in Human Neuroscience 11, (2017), 1-38. https://doi.org/10.3389/fnhum.2017.00038

J. F. Peters, Temporal Proximity of 1-cycles in CW Spaces. Time-Varying Cell Complexes, Fund. Contemp. Math. Sci 2, no. 2 (2021), 1-20.

J. F. Peters and T. Vergili, Fixed point property of amenable planar vortexes, Applied General Topology 22, no. 2 (2021), 385-397. https://doi.org/10.4995/agt.2021.15096

V. Puisséux, Recherches sur les fonctions algbriques, Journal de mathématiques pures et appliq 15 (1850), 365-480.

Ju. M. Smirnov, On proximity spaces, Math. Sb. (N.S.) 31, no. 73 (1952), 543-574 (English translation: Amer. Math. Soc. Trans. Ser. 2, 38 (1964), 5-35).

Ju. M. Smirnov, On proximity spaces in the sense of V. A. Efremovič, Math. Sb. (N.S.) 84, (1952), 895-898 (English translation: Amer. Math. Soc. Trans. Ser. 2, 38, (1964), 1-4). https://doi.org/10.1090/trans2/038/01

R. M. Switzer, Algebraic topology - homology and homotopy, Springer, Berlin, xii+526 pp, 2002. https://doi.org/10.1007/978-3-642-61923-6_8

K. Tanaka, Simple homotopy theory and nerve theorem for categories, Topology Appl. 291 (2021), 1-23. https://doi.org/10.1016/j.topol.2021.107609

E. Čech, Topological Spaces, John Wiley & Sons Ltd., London, 1966 (fr seminar, Brno, 1936-1939; rev. ed. Z. Frolik, M. Katĕtov).

R. Vanden Eynde, Historical evolution of the concept of homotopic paths, Arch. Hist. Exact Sci. 45, no.2 (1992), 127-188. https://doi.org/10.1007/BF00374251

F. Vigolo, The geometry and topology of wide ribbons, University of Oxford, UK, Balliol College, 207 pp, 2018 (Supervisor: Cornelia Druţu).

S. Willard, General Topology, Dover Pub., Inc., Mineola, NY, xii + 369pp, 1970.

[-]

recommendations

 

Este ítem aparece en la(s) siguiente(s) colección(ones)

Mostrar el registro completo del ítem