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)
D-spaces. (English) Zbl 0983.54024

For a space (X,τ), a function U:Xτ such that each xU(x) is called an open neighborhood assignment (ONA). (X,τ) is a D-space if for each ONA, U, there exists a closed discrete DX such that {U(x)xD}=U(D)=X. For an ONA U:xτ and DX, D is said to be U-sticky if D is closed discrete and xU(D) whenever U(x)D. Among other results, it is proved that

(1) Box products of scattered spaces of height 1 are D-spaces,

(2) A subspace of a linearly ordered space is a D-space iff it has no closed stationary subset (a harder proof of this result is due to van Douwen),

(3) A subspace of the product of finitely many ordinals is a D-space iff it is metacompact iff it has no closed stationary subsets.

MSC:
54D20Noncompact covering properties (paracompact, Lindelöf, etc.)
54E20Stratifiable spaces, cosmic spaces, etc.
54F05Linearly, generalized, and partial ordered topological spaces