zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Manifolds: Hausdorffness versus homogeneity. (English) Zbl 1140.57014

In this work an n-manifold is a topological space that is locally homeomorphic to n . The objective is to analyze the relationship between homogeneity and being Hausdorff among such spaces. Is homogeneity a sufficient condition to characterize those manifolds that are Hausdorff? The authors exhibit two examples which show that the answer is no.

The first example, called the “complete feather,” was first defined by A. Haefliger and G. Reeb [Enseign. Math., II. Sér. 3, 107–125 (1957; Zbl 0079.17101)]. This space is a connected non-Hausdorff homogeneous 1-manifold which is neither separable nor Lindelöf. It is contractible but it does not admit a strong deformation retraction to any of its points. The second example is called the “everywhere doubled line.” It is a connected, homogeneous and separable 1-manifold that is neither Hausdorff nor Lindelöf.

MSC:
57N99Topological manifolds
54D10Lower separation axioms (T 0 T 3 , etc.)
54E52Baire category, Baire spaces