Representation of relatively uniform and order convergence topologies by an inductive limit
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2013), pp. 9-20 Cet article a éte moissonné depuis la source Math-Net.Ru

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Using the concept of a topological affine space, it is proved that a partially ordered topological linear space associated with relatively uniform and order convergence can be represented by an inductive limit of its subspaces.
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V. M. Fedorov. Representation of relatively uniform and order convergence topologies by an inductive limit. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2013), pp. 9-20. http://geodesic.mathdoc.fr/item/VMUMM_2013_5_a1/

[1] Burbaki N., Integrirovanie. Mery, integrirovanie mer, Nauka, M., 1967 | MR

[2] Burbaki N., Topologicheskie vektornye prostranstva, IL, M., 1959

[3] Kantorovich L.V., Vulikh B.Z., Pinsker A.G., Funktsionalnyi analiz v poluuporyadochennykh prostranstvakh, GITTL, M.; L., 1950 | MR

[4] Burbaki N., Osnovnye struktury analiza. Teoriya mnozhestv, Mir, M., 1965

[5] Birkhoff G., “Moore–Smith convergence in general topology”, Ann. Math., 38:1 (1937), 39–56 | DOI | MR

[6] Birkgof G., Teoriya reshetok, Nauka, M., 1984 | MR

[7] Vulikh B.Z., Vvedenie v teoriyu poluuporyadochennykh prostranstv, Nauka, M., 1961 | MR

[8] Fedorov V.M., “O maksimalnoi topologii skhodimosti v poluuporyadochennom prostranstve”, K 190-letiyu P. L. Chebysheva, Sovremennye problemy matematiki i mekhaniki, VII, no. 1, Izd-vo MGU, M., 2011, 110–136

[9] Gordon H., “Relative uniform convergence”, Math. Ann., 153 (1964), 418–427 | DOI | MR

[10] Klee V.L., “Convex sets in linear spaces”, Duke Math. J., 18 (1951), 443–466 | DOI | MR

[11] Frechet M., Les espaces abstraits, Gauthier–Villars, P., 1928 | MR

[12] Burbaki N., Obschaya topologiya. Osnovnye struktury, Nauka, M., 1968 | MR

[13] Fedorov V.M., “Faktornormalnye klinya poluuporyadochennykh prostranstv”, Vestn. Mosk. un-ta. Matem. Mekhan., 2008, no. 4, 26–36

[14] Namioka I., Partially ordered linear topological spaces, Mem. Amer. Math. Soc., 24, 1957 | MR

[15] Shefer Kh., Topologicheskie vektornye prostranstva, Mir, M., 1971 | MR

[16] Klee V.L., “The support property of a convex set in linear normed space”, Duke Math. J., 15 (1948), 767–772 | DOI | MR

[17] Kelley G., Namioka I., Linear topological spases, Springer-Verlag, N. Y.–Heidelberg–Berlin, 1963 | MR