Note however that weak and strong topologies are always distinct in infinite-dimensional space.

There is also a generalization to infinite-dimensional spaces.

In infinite-dimensional spaces, not all linear maps are continuous.

Since G therefore has an infinite-dimensional space of pseudocharacters, it cannot be boundedly generated.

By contrast, in many problems the number of possibilities is unbounded and then one must use infinite-dimensional spaces to represent them.

In an infinite-dimensional space, the column-vector representation of A would be a list of infinitely many complex numbers.

This is however false for any infinite-dimensional normed space, as shown by the example of discontinuous linear maps.

In general, this is an infinite-dimensional space.

To deal with infinite-dimensional spaces, we must generalize the above definition to include infinite basis sets.

God, Willink argues, exists on a complete separate, infinite-dimensional space completely removed from these three planes.