Connecting direct limit topologies with metrics on infinite-dimensional manifolds

Katsuro Sakai

Compositio Mathematica (1992)

  • Volume: 81, Issue: 2, page 237-245
  • ISSN: 0010-437X

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Sakai, Katsuro. "Connecting direct limit topologies with metrics on infinite-dimensional manifolds." Compositio Mathematica 81.2 (1992): 237-245. <http://eudml.org/doc/90138>.

@article{Sakai1992,
author = {Sakai, Katsuro},
journal = {Compositio Mathematica},
keywords = {-manifold; -manifold; -manifold; Hilbert cube; -manifold; homotopy equivalent; homeomorphism},
language = {eng},
number = {2},
pages = {237-245},
publisher = {Kluwer Academic Publishers},
title = {Connecting direct limit topologies with metrics on infinite-dimensional manifolds},
url = {http://eudml.org/doc/90138},
volume = {81},
year = {1992},
}

TY - JOUR
AU - Sakai, Katsuro
TI - Connecting direct limit topologies with metrics on infinite-dimensional manifolds
JO - Compositio Mathematica
PY - 1992
PB - Kluwer Academic Publishers
VL - 81
IS - 2
SP - 237
EP - 245
LA - eng
KW - -manifold; -manifold; -manifold; Hilbert cube; -manifold; homotopy equivalent; homeomorphism
UR - http://eudml.org/doc/90138
ER -

References

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  1. [Du] Dugundji, J.: Locally equiconnected spaces and absolute neighborhood retracts, Fund. Math57 (1965), 187-193. Zbl0151.30301MR184202
  2. [Ch] Chapman, T.A.: Dense sigma-compact subsets of infinite-dimensional manifolds, Trans. Amer. Math. Soc.154 (1971), 399-426. Zbl0208.51903MR283828
  3. [Ge] Geoghegan, R. (ed.): Open problems in infinite-dimensional topology, Topology Proc.4 (1979), 287-330. Zbl0448.57001MR583711
  4. [He1] Heisey, R.E.: Partitions of unity and a closed embedding theorem for (Cb, b*)-manifolds, Trans. Amer. Math. Soc.206 (1975), 281-294. Zbl0301.58009MR397767
  5. [He2] Heisey, R.E.: Manifolds modelled on the direct limit of Hilbert cubes, in J.C. Cantrell (ed.), Geometric Topology, Academic Press, New York (1979), 609-619. Zbl0477.57009MR537754
  6. [Ke] Kelly, J.C.: Bitopological spaces, Proc. London Math. Soc. (3) 13 (1963), 71-89. Zbl0107.16401MR143169
  7. [Pa] Palais, R.S.: Banach manifolds of fiber bundle sections, Actes Congrès Intern. Math., Nice, 1970, vol. 2, Gauthier-Villars, Paris (1971), 243-249. Zbl0326.58008MR448405
  8. [vM] van Mill, J.: Infinite-Dimensional Topology, Prerequisites and Introduction, North-Holland Math. Library43, Elsevier Sci. Publ., Amsterdam (1989). Zbl0663.57001MR977744
  9. [Sa1] Sakai, K.: Embeddings of infinite-dimensional manifold pairs and remarks stability and deficiency, J. Math. Soc. Japan29 (1977), 262-280. Zbl0365.57003MR458433
  10. [Sa2] Sakai, K.: On R∞-manifolds and Q∞-manifolds, Topology Appl.18 (1984), 69-79. Zbl0568.57014
  11. [Sa3] Sakai, K.: Fine homotopy equivalences of metric simplicial complexes, Bull. Polish Acad. Sci. Math.34 (1986), 89-97. Zbl0609.55005MR850319
  12. [Sa4] Sakai, K.: Combinatorial infinite-dimensional manifolds and R∞-manifolds, Topology Appl.26 (1987), 287-300. Zbl0652.58007
  13. [Sa5] Sakai, K.: On topologies of triangulated infinite-dimensional manifolds, J. Math. Soc. Japan39 (1987), 287-300. Zbl0652.58007MR879930
  14. [Sa6] Sakai, K.: Simplicial complexes triangulating infinite-dimensional manifolds, Topology Appl.29 (1988), 167-183. Zbl0651.57013MR949367
  15. [Sa7] Sakai, K.: The space of Lipschitz maps from a compactum to an absolute neighborhood LIP extensor, Fund. Math., in press. Zbl0749.58013MR1122276
  16. [Sa8] Sakai, K.: A Q∞-manifold topology of the space of Lipschitz maps, preprint. Zbl0789.58018
  17. [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. MR1078666

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