Space
Linear space
For arbitrary elements
of space 
and scalar numbers 
,
- A single element
exists satisfying 
is denominated as a null element
Inner product space
Consider arbitrary elements
in linear space 
where the complex number 
is defined, satisfying:
scalar
is called the inner product.Distance space
Consider arbitrary elements
in linear space 
where the real number 
is defined, satisfying:
is denominated as the distance between 
.Normed space
Consider an arbitrary element
in linear space 
where the real number 
is defined, satisfying:
scalar
is denominated as the norm of 
.Convergence
The sequence
of the elements of a normed space 
,
satisfying
exists.
Cauchy sequence
Properties
Convergent sequence
Cauchy sequenceCompleteness
When an arbitrary Cauchy sequence in space
becomes a convergent sequence.Banach space
A complete normed space
Hilbert space
A complete inner product normed space
space
a measurable complex function in 
real number,
[0]Top