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

How to cite


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

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 = {},
volume = {81},
year = {1992},

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 -
ER -


  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

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.