# T-open

• Apr 9th 2010, 09:16 AM
HoneyPi
T-open
Hi,

my book says that "... If we wish to emphasize the topology T, then we refer to U as T-open, ..."

Does this then mean that U fullfils the topology properties?

Honey $\pi$
• Apr 9th 2010, 09:28 AM
Opalg
Quote:

Originally Posted by HoneyPi
Hi,

my book says that "... If we wish to emphasize the topology T, then we refer to U as T-open, ..."

Does this then mean that U fullfils the topology properties?

It means that U is an open set in the topology T. It's the topology T that has to fulfil the topology properties. The set U just has to satisfy the condition of being one of the open sets in that topology.
• Apr 9th 2010, 09:49 AM
HoneyPi
Quote:

Originally Posted by Opalg
It means that U is an open set in the topology T. It's the topology T that has to fulfil the topology properties. The set U just has to satisfy the condition of being one of the open sets in that topology.

Honey $\pi$