If a space is compact, then so are all its quotient spaces.

The quotient space where the natural numbers on the real line are identified as a single point is not first countable.

To this end you can use the notion of a quotient space:

There is, however, no reason to expect such quotient spaces to be manifolds.

An important example of a functional quotient space is a L space.

If is empty, then the quotient space is an orbifold.

So we quotient space (or "glue together") antipodal points on the surface of the ball.

The space X is a quotient space or identification space.

This can be visualized as gluing these points together in a single point, forming a quotient space.

The quotient space is a generalized space of normal vectors.

The resulting quotient space is called the lens space .

This criterion is constantly used when studying quotient spaces.

In general, quotient spaces are ill-behaved with respect to separation axioms.

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

Specifically, the rose is the quotient space of the graph obtained by collapsing a spanning tree.

Heuristically, one often thinks of a pair as being akin to the quotient space .

The Fuchsian model of R is the quotient space .

If , then the quotient space is also called the mapping torus of .

The cosets of the quotient space have the standard fundamental polygon as a representative element.

Gluing edges of polygons is a special kind of quotient space process.

The quotient space is already endowed with a vector space structure by the construction of the previous section.

The quotient space M/G has points that correspond to the cells of the decomposition.

However, it is much more elegant to just work with the quotient space of vector field configurations by gauge transformations.

The quotient space W/V can also be made into a representation of G.

The notion is similar to that of a quotient group or quotient space, but in the categorical setting.