Determine whether or not the general version of the Intermediate Theorem holds when the range $\displaystyle \Re$ is given each of the following topologies
i. The trivial topology
ii. The discrete topology
iii. The finite complement topology
Determine whether or not the general version of the Intermediate Theorem holds when the range $\displaystyle \Re$ is given each of the following topologies
i. The trivial topology
ii. The discrete topology
iii. The finite complement topology