Theorem

Ifis a connected subset ofand there exists a setsuch thatthen is connected.

Proof

Supposeis disconnected, thenfor setsfor open setsand

Sinceis a connected subset ofeitheror

Supposethenis closed andhence

This contradictshenceis connected.

Call Us 07766496223

Theorem

Ifis a connected subset ofand there exists a setsuch thatthen is connected.

Proof

Supposeis disconnected, thenfor setsfor open setsand

Sinceis a connected subset ofeitheror

Supposethenis closed andhence

This contradictshenceis connected.