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![]() For compact 2-dimensional surfaces without boundary, if every loop can be continuously tightened to a point, then the surface is topologically homeomorphic to a 2-sphere (usually just called a sphere). The Poincaré conjecture, proved by Grigori Perelman, asserts that the same is true for 3-dimensional spaces. | |
Type | Theorem |
---|---|
Field | Geometric topology |
Statement | Every simply connected, closed 3-manifold is homeomorphic to the 3-sphere. |
Conjectured by | Henri Poincaré |
Conjectured in | 1904 |
First proof by | Grigori Perelman |
First proof in | 2006 |
Implied by | |
Open problem | No |
Generalizations | Generalized Poincaré conjecture |
The Template:Infobox mathematical statement generates a right-hand side infobox, based on the specified parameters. To use this template, copy the following code in your article and fill in as appropriate:
{{Infobox mathematical statement
| name =
| image =
| caption =
| type =
| field =
| statement =
| symbolic statement =
| conjectured by =
| conjecture date =
| first stated by =
| first stated in =
| first proof by =
| first proof date =
| open problem =
| known cases =
| implied by =
| equivalent to =
| generalizations =
| consequences =
}}
All parameters are optional.
name
Strong multiplicity one theorem
, Zorn's lemma
. Defaults to page name.image
xxx.svg
.caption
type
Theorem
, Conjecture
, Lemma
, Postulate
, Axiom
.field
Number theory
, Algebraic geometry and algebraic topology
.statement
symbolic statement
conjectured by
conjectured date
first stated by
first stated date
first proof by
first proof date
open problem
Yes
or No
, though something more specific could be put here (e.g. Only one example known
, etc.)known cases
For all function fields
or For all r > 3
).implied by
equivalent to
generalizations
consequences
Infobox for a logical statement in mathematics that can either be true or false. Can be used to describe theorems, conjectures, lemmas, postulates, and axioms.
Parameter | Description | Type | Status | |
---|---|---|---|---|
Title style | titlestyle | Inline CSS to style the title parameter. | String | optional |
Name | name | Name of the mathematical statement that appears at the top of the infobox.
| Page name | suggested |
Image | image | Image representing the mathematical statement. | File | suggested |
Image size | image_size imagesize | How large the image should be. | String | suggested |
Alternative text | alt | Alternative text describing an image, which is spoken out loud by screen reader devices | String | suggested |
Caption | caption | Descriptive text that appears below the image. | Unknown | suggested |
Type | type | Type of mathematical statement
| Content | suggested |
Field | field | One or more branch that the mathematical statement falls under
| Unknown | suggested |
Statement | statement | The mathematical statement. | Content | suggested |
Symbolic statement | symbolic statement | A symbolic version of the mathematical statement when a prose version is already given. | Content | suggested |
Conjectured by | conjectured by | Name of person(s) who first posed the statement. | Content | suggested |
Conjectured in | conjecture date | Date(s) of when the statement was first posed. | Content | suggested |
First stated by | first stated by | Name of person(s) who first posed the statement (alternative to using the word "conjectured"). | Content | suggested |
First stated in | first stated date | Date(s) of when the statement was first posed (alternative to using the word "conjectured"). | Content | suggested |
First proof by | first proof by | Name of person(s) who first proved the statement. | Content | suggested |
First proof in | first proof date | Date(s) of when the statement was first proven. | Content | suggested |
Implied by | implied by | Statement(s) that imply the current one. | Content | suggested |
Open problem | open problem | Is this an open problem? Typical values are Yes or No, though something more specific could be put here.
| String | suggested |
Known cases | known cases | The cases for which the statement is known. | Unknown | suggested |
Equivalent to | equivalent to | Statement(s) that both imply and are implied by the current one. | Content | suggested |
Generalizations | generalizations | Statement(s) that generalize the current one. | Content | suggested |
Consequences | consequences | Statement(s) that are implied by the current one. | Content | suggested |