Properties of Suslin Sets
- Every Borel set is a Suslin set.
- The collection of all Suslin sets is closed under countable unions and countable intersection.
- Not all Suslin sets are Borel sets (in non-trivial metric spaces such as ).
- If A is a subset of a Polish space then A is a Suslin set if and only if it is an analytic set.
- In a Polish space, any Suslin set is universally measurable.
Read more about this topic: Suslin Set
Famous quotes containing the words properties of, properties and/or sets:
“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)
“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)
“It is time to be old,
To take in sail:—
The god of bounds,
Who sets to seas a shore,
Came to me in his fatal rounds,
And said: ‘No more!’”
—Ralph Waldo Emerson (1803–1882)