Properties
Let be a function such that X and Y are topological spaces.
- If is continuous, it need not be quasi-open. Conversely if is quasi-open, it need not be continuous.
- If is open, then is quasi-open.
- If is a local homeomorphism, then is quasi-open.
- If and are both quasi-open (such that all spaces are topological), then the function composition is quasi-open.
Read more about this topic: Quasi-open Map
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“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)
“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)