contractible

In particular, the universal covering of such a space is contractible.

These spaces are of interest in their own right, despite typically being contractible.

Thus, on a contractible domain, every closed form is exact.

A contractible space is precisely one with the homotopy type of a point.

In particular, if C has an initial or final object, its nerve is contractible.

The cone on a space X is always contractible.

In fact, these satisfy the much stronger property of being locally contractible.

For example, an open ball is a contractible manifold.

An epidemic is an outbreak of a contractible disease that spreads through a human population.

Every contractible space is path connected and thus also connected.

Intuitively, a contractible space is one that can be continuously shrunk to a point.

It follows that all the homotopy groups of a contractible space are trivial.

Therefore any space with a nontrivial homotopy group cannot be contractible.

There exists a contractible space on which acts freely.

Since the half-plane is contractible, all bundle structures are trivial.

In mathematics, a fake 4-ball is a compact contractible topological 4-manifold.

The house with two rooms is a contractible 2-complex that is not collapsible.

The unit sphere in an infinite-dimensional Hilbert space is contractible.

The house with two rooms is standard example of a space which is contractible, but not intuitively so.

A set in is called -convex if its intersection with any complex line is contractible.

The local homomorphisms are all injective for a covering by contractible open sets.

Any star domain is a contractible set, via a straight-line homotopy.

In particular, if X is a connected contractible space, then all its homology groups are 0, except .

A quotient space of a simply connected or contractible space need not share those properties.

One can ask whether all contractible manifolds are homeomorphic to a ball.