?

Topology

Free Version

Upgrade subject to access all content

Moderate

Identifying Nets

TOPO-X4G5ID

Let $X$ be a topological space, which is also an algebra (addition and multiplication of elements in $X$ are defined, as well as multiplication by scalars). Let $A$ and $B$ be directed sets.

If $a:A\to X$, $b:A\to X$ and $c:B\to X$ are nets in $X$, which of the following are also nets in $X$? Select ALL that apply.

A

$a+b$

B

$a+c$

C

$a-b$

D

$b\cdot c$

E

$2a-3b$

F

$\pi c^2$

G

$P_n(a)$ where $P_n$ is a polynomial of degree $n$

H

$a+2b-4c$