@article{CM_1992__81_2_237_0, author = {Sakai, Katsuro}, title = {Connecting direct limit topologies with metrics on infinite-dimensional manifolds}, journal = {Compositio Mathematica}, pages = {237--245}, publisher = {Kluwer Academic Publishers}, volume = {81}, number = {2}, year = {1992}, mrnumber = {1145808}, zbl = {0754.57016}, language = {en}, url = {http://www.numdam.org/item/CM_1992__81_2_237_0/} }
TY - JOUR AU - Sakai, Katsuro TI - Connecting direct limit topologies with metrics on infinite-dimensional manifolds JO - Compositio Mathematica PY - 1992 SP - 237 EP - 245 VL - 81 IS - 2 PB - Kluwer Academic Publishers UR - http://www.numdam.org/item/CM_1992__81_2_237_0/ LA - en ID - CM_1992__81_2_237_0 ER -
Sakai, Katsuro. Connecting direct limit topologies with metrics on infinite-dimensional manifolds. Compositio Mathematica, Tome 81 (1992) no. 2, pp. 237-245. http://www.numdam.org/item/CM_1992__81_2_237_0/
[Du] Locally equiconnected spaces and absolute neighborhood retracts, Fund. Math 57 (1965), 187-193. | MR | Zbl
:[Ch] Dense sigma-compact subsets of infinite-dimensional manifolds, Trans. Amer. Math. Soc. 154 (1971), 399-426. | MR | Zbl
:[Ge] Geoghegan, R. (ed.): Open problems in infinite-dimensional topology, Topology Proc. 4 (1979), 287-330. | MR | Zbl
[He1] Partitions of unity and a closed embedding theorem for (Cb, b*)-manifolds, Trans. Amer. Math. Soc. 206 (1975), 281-294. | MR | Zbl
:[He2] Manifolds modelled on the direct limit of Hilbert cubes, in J.C. Cantrell (ed.), Geometric Topology, Academic Press, New York (1979), 609-619. | MR | Zbl
:[Ke] Bitopological spaces, Proc. London Math. Soc. (3) 13 (1963), 71-89. | MR | Zbl
:[Pa] Banach manifolds of fiber bundle sections, Actes Congrès Intern. Math., Nice, 1970, vol. 2, Gauthier-Villars, Paris (1971), 243-249. | MR | Zbl
:[vM] Infinite-Dimensional Topology, Prerequisites and Introduction, North-Holland Math. Library 43, Elsevier Sci. Publ., Amsterdam (1989). | MR | Zbl
:[Sa1] Embeddings of infinite-dimensional manifold pairs and remarks stability and deficiency, J. Math. Soc. Japan 29 (1977), 262-280. | MR | Zbl
:[Sa2] On R∞-manifolds and Q∞-manifolds, Topology Appl. 18 (1984), 69-79. | Zbl
:[Sa3] Fine homotopy equivalences of metric simplicial complexes, Bull. Polish Acad. Sci. Math. 34 (1986), 89-97. | MR | Zbl
:[Sa4] Combinatorial infinite-dimensional manifolds and R∞-manifolds, Topology Appl. 26 (1987), 287-300. | Zbl
:[Sa5] On topologies of triangulated infinite-dimensional manifolds, J. Math. Soc. Japan 39 (1987), 287-300. | MR | Zbl
:[Sa6] Simplicial complexes triangulating infinite-dimensional manifolds, Topology Appl. 29 (1988), 167-183. | MR | Zbl
:[Sa7] The space of Lipschitz maps from a compactum to an absolute neighborhood LIP extensor, Fund. Math., in press. | MR | Zbl
:[Sa8] A Q∞-manifold topology of the space of Lipschitz maps, preprint. | Zbl
:[We] West, J.E. (ed.): Open problems in infinite-dimensional topology, in J. van Mill and G.M. Reed (eds), Open Problems in Topology, Elsevier Sci. Publ., Amsterdam (1990), 523-597. | MR