Category:Pages requiring proofs: Easy proofs

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Pages in category "Pages requiring proofs: Easy proofs"

The following 39 pages are in this category, out of 39 total.

A

A cap (B-C) = (A cap B) - C
A linear map is injective if and only if the image of every non-zero vector is a non-zero vector
A pair of identical elements is a singleton
A proper vector subspace of a topological vector space has no interior
A set is open if and only if every point in the set has an open neighbourhood contained within the set
A subset of a topological space is disconnected if and only if it can be covered by two non-empty-in-the-subset and disjoint-in-the-subset sets that are open in the space itself
A topological space is connected if and only if the only sets that are both open and closed in the space are the entire space itself and the emptyset
A topological space is disconnected if and only if it is homeomorphic to a disjoint union of two or more non-empty topological spaces
A topological space is disconnected if and only if there exists a non-constant continuous function from the space to the discrete space on two elements
A-(A-B) = A cap B

C

D

Demonstrating why category arrows are best thought of as arrows and not functions

D cont.

E

E cont.

Every surjective map gives rise to an equivalence relation

H

Hausdorff space

I

If an inner product is non-zero then both arguments are non-zero

M

P

S

Subspace topology

T

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