Open subsets of LF-spaces

• Autorzy: Mine K. , Sakai K.
• Języki publikacji: EN

Abstrakty

EN

Let F = ind lim Fn be an infinite-dimensional LF-space with density dens F = r ( ≥ ℵo) such that some Fn is infinite-dimensional and dens Fn = r. It is proved that every open subset of F is homeomorphic to the product of an l2(r)-manifold and R∞ = ind lim Rn (hence the product of an open subset of l2(r) and R∞). As a consequence, any two open sets in F are homeomorphic if they have the same homotopy type.

Słowa kluczowe

EN

LF-space; density; open set; direct limit; K[infinity]; l2(r)-manifold; l2(r) x R[infinity]-manifold

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2008
• Tom: Vol. 56, no 1
• Strony: 25--37
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Mine K.

autor

Sakai K.

• Institute of Mathematics, University of Tsukuba, Tsukuba, 305-8571, Japan,

Bibliografia

• [1] R. D. Anderson and J. D. McCharen, On extending homeomorphisms to Frechet manifolds, Proc. Amer. Math. Soc. 25 (1970), 283-289.
• [2] C. Bessaga and A. Pełczyński, Selected Topics in Infinite-Dimensional Topology, Monogr. Mat. 58, Polish Sci. Publ., Warszawa, 1975.
• [3] R. E. Heisey, Manifolds modelled on the direct limit of lines, Pacific J. Math. 102 (1982), 47-54.
• [4] D. W. Henderson, Corrections and extensions of two papers about infinite-dimensional manifolds, General Topology Appl. 1 (1971), 321-327.
• [5] D. W. Henderson and R. M. Schori, Topological classification of infinite-dimensional manifolds by homotopy type, Bull. Amer. Math. Soc. 76 (1970), 121-124.
• [6] P. Mankiewicz, On topological, Lipschitz, and uniform classification of LF-spaces, Studia Math. 52 (1974), 109-142.
• [7] K. Sakai, On R∞-manifolds and Q∞-manifolds, Topology Appl. 18 (1984), 69-79.
• [8] H. H. Schaefer with M. P. Wolff, Topological Vector Spaces, 2nd ed., Grad. Texts in Math. 3, Springer, New York, 1999.
• [9] R. M. Schori, Topological stability of infinite-dimensional manifolds, Compos. Math. 23 (1971), 87-100.
• [10] H. Toruńczyk, Absolute retracts as factors of normed linear spaces, Fund. Math. 86 (1974), 53-67.
• [11] -, Characterizing Hilbert space topology, ibid. 111 (1981), 247-262.
• [12] A. Wilansky, Modern Methods in Topological Vector Spaces, McGraw-Hill, New York, 1978.