Category:Functional Analysis Theorems, lemmas and corollaries

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Pages in category "Functional Analysis Theorems, lemmas and corollaries"

The following 42 pages are in this category, out of 42 total.

1

UTLOC:1

A

A function is continuous if and only if the pre-image of every basis element is open
A monotonically increasing sequence bounded above converges
A proper vector subspace of a topological vector space has no interior
A sequence consisting of the nth terms of the sequences in a Cauchy sequence of elements in any little-L space is itself a Cauchy sequence of complex numbers
A set is bounded if and only if for all points in the space there is a positive real such that the distance from that point to any point in the set is less than the positive real

B

Borel sigma-algebra of the real line

C

E

E cont.

F

G

Given a Hilbert space and a non-empty, closed and convex subset then for each point in the space there is a closest point in the subset

I

I cont.

M

O

Operations on convergent sequences of real numbers

R

Reverse triangle inequality

T

W

Weierstrass approximation theorem

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