Topology

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Domain of a Net

TOPO-BQ4JME

Let $X$ be a topological space. You are told that the function $\,n:A\to X$ is a net.

Which of the following must be true? Select ALL that apply.

A

The set $A$ is the set of natural numbers $\{1,2,\ldots\}\!$.

B

The set $A$ is countable.

C

The set $A$ is directed.

D

For any two elements $a,b$ of $A\,$ one can find a $c\in A$ such that $c$ is smaller than (or equal to) both $a$ and $b$.

E

The set $A$ is the set of integers $\{0,1,-1,2,-2,\ldots\}\!$.

F

For any two elements $a,b$ of $A\,$ one can find a $c\in A$ such that $c$ is greater than (or equal to) both $a$ and $b$.