NETMaths
Log inStart free

Is this true?

Connected components are open

No — it is false.

The counterexample

with the usual topology

Components are singletons, which are not open. They are open exactly when the space is locally connected.

The kind of mistake this is

Property not inherited

A property assumed to pass to subobjects, quotients, or through a chain. It does not.

Drill statements like this
topologyconnectedness

Others that fail the same way

From Topology › Connectedness and components

ShareWhatsAppTelegram