In
geometric topology, a wild arc is an
embedding
In mathematics, an embedding (or imbedding) is one instance of some mathematical structure contained within another instance, such as a group that is a subgroup.
When some object X is said to be embedded in another object Y, the embedding is gi ...
of the
unit interval
In mathematics, the unit interval is the closed interval , that is, the set of all real numbers that are greater than or equal to 0 and less than or equal to 1. It is often denoted ' (capital letter ). In addition to its role in real analysis, ...
into 3-dimensional space not equivalent to the usual one in the sense that there does not exist an
ambient isotopy taking the arc to a straight line segment. found the first example of a wild arc, and found another example called the Fox-Artin arc whose
complement
A complement is something that completes something else.
Complement may refer specifically to:
The arts
* Complement (music), an interval that, when added to another, spans an octave
** Aggregate complementation, the separation of pitch-clas ...
is not
simply connected
In topology, a topological space is called simply connected (or 1-connected, or 1-simply connected) if it is path-connected and every path between two points can be continuously transformed (intuitively for embedded spaces, staying within the spac ...
.
See also
*
Wild knot
Wild, wild, wilds or wild may refer to:
Common meanings
* Wild animal
* Wilderness, a wild natural environment
* Wildness, the quality of being wild or untamed
Art, media and entertainment Film and television
* ''Wild'' (2014 film), a 2014 Am ...
*
Horned sphere
The Alexander horned sphere is a pathological object in topology discovered by .
Construction
The Alexander horned sphere is the particular embedding of a sphere in 3-dimensional Euclidean space obtained by the following construction, starting ...
Further reading
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{{Topology
Geometric topology