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The Alexandroff property and the preservation of strong uniform continuity

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The Alexandroff property and the preservation of strong uniform continuity

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Beer, G. (2010). The Alexandroff property and the preservation of strong uniform continuity. Applied General Topology. 11(2):117-133. https://doi.org/10.4995/agt.2010.1712

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Título: The Alexandroff property and the preservation of strong uniform continuity
Autor: Beer, Gerald
Fecha difusión:
Resumen:
[EN] In this paper we extend the theory of strong uniform continuity and strong uniform convergence, developed in the setting of metric spaces in, to the uniform space setting, where again the notion of shields plays a key ...[+]
Palabras clave: Strong uniform continuity , Strong uniform convergence , Preservation of continuity , Variational convergence , Bornology , The Alexandroff property , The Bartle property , Shield , Quasi-uniform convergence , Bornological uniform cover , Sticking topology
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.2010.1712
Editorial:
Universitat Politècnica de València
Versión del editor: https://doi.org/10.4995/agt.2010.1712
Tipo: Artículo

References

P. Alexandroff, Einf¨uhring in die Mengenlehre und die theorie der rellen Funktionen, Deutscher Verlag der Wissenschaften, Berlin, 1964

H. Attouch and R. Wets, Quantitative stability of variational systems: I. The epigraphical distance, Trans. Amer. Math. Soc. 328 (1991), 695-730.

G. Beer, Topologies on closed and closed convex sets, Kluwer Acad. Publ., Dordrecht, 1993. G. Beer, C. Costantini, and S. Levi, Bornological convergence and shields, preprint. G. Beer, C. Costantini, and S. Levi, Total boundedness in metrizable spaces, Houston J. Math., to appear. [+]
P. Alexandroff, Einf¨uhring in die Mengenlehre und die theorie der rellen Funktionen, Deutscher Verlag der Wissenschaften, Berlin, 1964

H. Attouch and R. Wets, Quantitative stability of variational systems: I. The epigraphical distance, Trans. Amer. Math. Soc. 328 (1991), 695-730.

G. Beer, Topologies on closed and closed convex sets, Kluwer Acad. Publ., Dordrecht, 1993. G. Beer, C. Costantini, and S. Levi, Bornological convergence and shields, preprint. G. Beer, C. Costantini, and S. Levi, Total boundedness in metrizable spaces, Houston J. Math., to appear.

G. Beer and S. Levi, Pseudometrizable bornological convergence is Attouch-Wets convergence, J. Convex Anal. 15 (2008), 439-453.

Beer, G., & Segura, M. (2009). Well-posedness, bornologies, and the structure of metric spaces. Applied General Topology, 10(1), 131-157. doi:10.4995/agt.2009.1793

N. Bouleau, Une structure uniforme sur un espace F(E, F), Cahiers Topologie Géom. Diff., 11 (1969), 207-214.

N. Dunford and J. Schwartz, Linear operators part I, Wiley Interscience, New York, 1988 H. Hogbe-Nlend, Bornologies and functional analysis, North-Holland, Amsterdam, 1977.

S.-T. Hu, Boundedness in a topological space, J. Math Pures Appl. 228 (1949), 287-320.

Rainwater, J. (1959). Spaces whose finest uniformity is metric. Pacific Journal of Mathematics, 9(2), 567-570. doi:10.2140/pjm.1959.9.567

S. Willard, General topology, Addison-Wesley, Reading, MA, 1970.

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