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1994-1995 | 146 | 1 | 31-58
Tytuł artykułu

The space of ANR’s in $ℝ^n$

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The hyperspaces $ANR(ℝ^n)$ and $AR(ℝ^n)$ in $2^{ℝ^n} (n ≥ 3)$ consisting respectively of all compact absolute neighborhood retracts and all compact absolute retracts are studied. It is shown that both have the Borel type of absolute $G_{δσ δ}$-spaces and that, indeed, they are not $F_{σ δσ }$-spaces. The main result is that $ANR(ℝ^n)$ is an absorber for the class of all absolute $G_{δσ δ}$-spaces and is therefore homeomorphic to the standard model space $Ω_3$ of this class.
Rocznik
Tom
146
Numer
1
Strony
31-58
Opis fizyczny
Daty
wydano
1994
otrzymano
1993-06-25
poprawiono
1993-10-05
poprawiono
1994-03-03
Twórcy
  • Department of Mathematics, The University of Oklahoma, 601 Elm Avenue, Room 423, Norman, Oklahoma 73019-0315, U.S.A., lrubin@nsfuvax.math.uoknor.edu
Bibliografia
  • [BGvM] J. Baars, H. Gladdines and J. van Mill, Absorbing systems in infinite-dimensional manifolds, Topology Appl. 50 (1993), 147-182.
  • [BP] C. Bessaga and A. Pełczyński, Selected Topics in Infinite-Dimensional Topology, PWN, Warszawa, 1975.
  • [BM] M. Bestvina and J. Mogilski, Characterizing certain incomplete infinite-dimensional retracts, Michigan Math. J. 33 (1986), 291-313.
  • [Bor] K. Borsuk, On some metrizations of the hyperspace of compact sets, Fund. Math. 41 (1954), 168-202.
  • [C1] R. Cauty, L'espace des pseudo-arcs d'une surface, Trans. Amer. Math. Soc. 331 (1992), 247-263.
  • [C2] R. Cauty, L'espace des arcs d'une surface, ibid. 332 (1992), 193-209.
  • [C3] R. Cauty, Les fonctions continues et les fonctions intégrables au sens de Riemann comme sous-espaces de $L^1$, Fund. Math. 139 (1991), 23-36.
  • [CDGvM] R. Cauty, T. Dobrowolski, H. Gladdines et J. van Mill, Les hyperespaces des rétractes absolus et des rétractes absolus de voisinage du plan, preprint.
  • [Cu1] D. W. Curtis, Hyperspaces of finite subsets as boundary sets, Topology Appl. 22 (1986), 97-107.
  • [Cu2] D. W. Curtis, Hyperspaces of non-compact metric spaces, Compositio Math. 40 (1986), 139-152.
  • [CN] D. W. Curtis and N. T. Nhu, Hyperspaces of finite subsets which are homeomorphic to $ℵ_0$-dimensional linear metric spaces, Topology Appl. 19 (1985), 251-260.
  • [DvMM] J. J. Dijkstra, J. van Mill and J. Mogilski, The space of infinite-dimensional compacta and other topological copies of $(ℓ^2_f)^ω$, Pacific J. Math. 152 (1992), 255-273.
  • [DM] T. Dobrowolski and W. Marciszewski, Classification of function spaces with the pointwise topology determined by a countable dense set, preprint.
  • [DR] T. Dobrowolski and L. R. Rubin, The hyperspaces of infinite-dimensional compacta for covering and cohomological dimension are homeomorphic, Pacific J. Math. 164 (1994), 15-39.
  • [GvM] H. Gladdines and J. van Mill, Hyperspaces of Peano continua of euclidean spaces, Fund. Math. 142 (1993), 173-188.
  • [Kur1] K. Kuratowski, Sur une méthode de métrisation complète de certains espaces d'ensembles compacts, ibid. 43 (1956), 114-138.
  • [Kur2] K. Kuratowski, Topology I, Academic Press, New York and London, 1966.
  • [MS] S. Mardešić and J. Segal, Shape Theory, North-Holland, Amsterdam, 1982.
  • [vM] J. van Mill, Infinite-Dimensional Topology: prerequisites and introduction, North-Holland, Amsterdam, 1989.
  • [SR] J. Saint Raymond, Fonctions boréliennes sur un quotient, Bull. Sci. Math. (2) 100 (1976), 141-147.
  • [Tor] H. Toruńczyk, Concerning locally homotopy negligible sets and characterization of $l_2$-manifolds, Fund. Math. 101 (1978), 93-110.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv146i1p31bwm
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