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Fσ set∗
rspuzio†
2013-03-21 17:56:24
A subset of a topological space is called a Fσ set if it equals the union of a
countable collection of closed sets.
The complement of a Fσ set is a Gδ set.
For instance, the X set of all points (x, y) in the plane such that either y = 0
or x/y is rational is an Fσ set because it can be expressed as the union of a
countable set of lines:
[
X = {(x, 0) | x ∈ R} ∪
{(ry, y) | y ∈ R}
r∈Q
∗ hFsigmaSeti created: h2013-03-21i by: hrspuzioi version: h36215i Privacy setting: h1i
hDefinitioni h54A05i
† This text is available under the Creative Commons Attribution/Share-Alike License 3.0.
You can reuse this document or portions thereof only if you do so under terms that are
compatible with the CC-BY-SA license.
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