Examples of 'closed subspace' in a sentence
Meaning of "closed subspace"
closed subspace - a mathematical concept referring to a subset of a topological space that is also a topological space with respect to the induced topology
How to use "closed subspace" in a sentence
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closed subspace
Every closed subspace of an orthocompact space is orthocompact.
Every quotient of a reflexive space by a closed subspace is reflexive.
Every closed subspace of a paracompact space is paracompact.
Any subspace and any quotient space by a closed subspace of a nuclear space is nuclear.
A closed subspace of a complete space is complete.
A quotient of a Fréchet space by a closed subspace is a Fréchet space.
Show that closed subspace of a complete metric space is complete.
Let us show the equivalent condition on y when C M is a closed subspace.
A closed subspace of a Fréchet space is a Fréchet space.
For every separable Banach space, there is a closed subspace of such that.
This is a closed subspace of c, and so again a Banach space.
But there are some modifications needed, To define a subrepresentation we now need a closed subspace.
However, a closed subspace must be Lindelöf.
The following are equivalent, The space X does not contain a closed subspace isomorphic to ℓ1.
It is a closed subspace of X, so compact.
See also
The space E ( M ) is always topologically equivalent to a closed subspace of the Cantor set.
Likewise it is called a closed subspace if the injection ι { \ displaystyle \ iota } is a closed map.
In other words, the range of a continuous projection P { \ displaystyle P } must be a closed subspace.
Paracompactness is weakly hereditary, i.e. every closed subspace of a paracompact space is paracompact.
It is a closed subspace of ℓ ∞, hence a Banach space.
If f is the inclusion of a closed subspace X ⊂ Y then f ∗ is exact.
