On the Euler characteristic of compact complete locally affine spaces. II
نویسندگان
چکیده
منابع مشابه
On the Euler Characteristic of Compact Complete Locally Affine Spaces. Ii by Louis Auslander
The main result of this paper may be stated very simply: A compact complete locally affine space has Ruler characteristic zero. In [ l ] we showed that if the radical of the fundamental group is nontrivial then the Euler characteristic is zero. Hence all that remains is to show that the radical of the fundamental group is indeed nontrivial. To do this one may as well limit oneself to the study ...
متن کاملOn Locally Compact Metrisable Spaces
In Theorem 1 the word metric may be replaced, on the one hand, by regular, on the other, by complete metric. This theorem is of interest chiefly because of the similar well known characterizations of the class of all compact metrisable spaces and of the class of all metrisable spaces which are homeomorphic to complete metric spaces.§ The method of proof also relates it to the two characterizati...
متن کاملHyperbolization of locally compact non-complete metric spaces
By a hyperbolization of a locally compact non-complete metric space (X, d) we mean equipping X with a Gromov hyperbolic metric dh so that the boundary at infinity ∂∞X of (X, dh) can be identified with the metric boundary ∂X of (X, d) via a quasisymmetric map. The aim of this note is to show that the Gromov hyperbolic metric dh, recently introduced by the author, hyperbolizes the space X. In add...
متن کاملLocally Compact, Ω1-compact Spaces
This paper is centered on an extremely general problem: Problem. Is it consistent (perhaps modulo large cardinals) that a locally compact space X must be the union of countably many ω-bounded subspaces if every closed discrete subspace of X is countable [in other words, if X is ω1-compact]? A space is ω-bounded if every countable subset has compact closure. This is a strengthening of countable ...
متن کاملOne-point extensions of locally compact paracompact spaces
A space $Y$ is called an {em extension} of a space $X$, if $Y$ contains $X$ as a dense subspace. Two extensions of $X$ are said to be {em equivalent}, if there is a homeomorphism between them which fixes $X$ point-wise. For two (equivalence classes of) extensions $Y$ and $Y'$ of $X$ let $Yleq Y'$, if there is a continuous function of $Y'$ into $Y$ which fixes $X$ point-wise. An extension $Y$ ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1961
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1961-10642-3