On the topological structure of the Levi-Civita field

Alling, 1987 Berz, 1996, Calculus and numerics on Levi-Civita fields, 19 Berz, 2000, Analytical and computational methods for the Levi-Civita fields, 21 Berz, 2003, Cauchy Theory on Levi-Civita Fields, vol. 319 Bourbaki, 1966 Conway, 1990 Davidson, 2002 Fleming, 1987 Krull, 1932, Allgemeine Bewertungstheorie, J. Reine Angew. Math., 167, 160, 10.1515/crll.1932.167.160 Levi-Civita, 1892, Sugli infiniti ed infinitesimi attuali quali elementi analitici, Atti Ist. Veneto Sc. Lett. Art., 7a, 1765 Levi-Civita, 1898, Sui numeri transfiniti, Rend. Accad. Lincei, 5a, 91 Priess-Crampe, 1983 Ribenboim, 1992, Fields: algebraically closed and others, Manuscripta Math., 75, 115, 10.1007/BF02567077 Rudin, 1987 Rudin, 1991 Schikhof, 1985 K. Shamseddine, New elements of analysis on the Levi-Civita field, PhD thesis, Michigan State University, East Lansing, Michigan, USA, 1999, also Michigan State University report MSUCL-1147 Shamseddine, 1996, Exception handling in derivative computation with non-Archimedean calculus, 37 Shamseddine, 2000, Convergence on the Levi-Civita field and study of power series, 283 Shamseddine, 2002, Intermediate values and inverse functions on non-Archimedean fields, Int. J. Math. Math. Sci., 30, 165, 10.1155/S0161171202013030 Shamseddine, 2003, Measure Theory and Integration on the Levi-Civita Field, vol. 319 Shamseddine, 2005, Analytical properties of power series on Levi-Civita fields, Ann. Math. Blaise Pascal, 12, 309, 10.5802/ambp.209 Shamseddine, 2006, Generalized power series on a non-Archimedean field, Indag. Math., 17, 457, 10.1016/S0019-3577(06)80044-3 Shamseddine, 2007, Intermediate value theorem for analytic functions on a Levi-Civita field, Bull. Belg. Math. Soc. Simon Stevin, 14, 1001, 10.36045/bbms/1197908910 Shamseddine, 2001, One-dimensional optimization on non-Archimedean fields, J. Nonlinear Convex Anal., 2, 351 Shamseddine, 2003, Constrained second order optimization on non-Archimedean fields, Indag. Math., 14, 81, 10.1016/S0019-3577(03)90073-5