- is
countable if
either it is
finite or it can be made in one to one
correspondence with the set of
natural numbers. Equivalently, a set is
countable if...
- second-
countable space is said to
satisfy the
second axiom of
countability. Like
other countability axioms, the
property of
being second-
countable restricts...
- Fréchet–Urysohn space. First-
countability is
strictly weaker than second-
countability.
Every second-
countable space is first-
countable, but any
uncountable discrete...
- mathematics, an
axiom of
countability is a
property of
certain mathematical objects that ****erts the
existence of a
countable set with
certain properties...
-
determined by its
values on the
countable dense subset.
Contrast separability with the
related notion of
second countability,
which is in
general stronger...
- ) = 0. {\displaystyle \mu (\varnothing )=0.}
Countable additivity (or σ-additivity): For all
countable collections { E k } k = 1 ∞ {\displaystyle...
- are
countable.
Proof of
first theorem: If P(α) = ∅ for some
index α, then P′ is the
countable union of
countable sets. Therefore, P′ is
countable. The...
- in Wiktionary, the free dictionary. In linguistics, a
count noun (also
countable noun) is a noun that can be
modified by a
quantity and that
occurs in...
-
ordered set X is said to
satisfy the
countable chain condition, or to be ccc, if
every strong antichain in X is
countable.
There are
really two conditions:...
- set does not
necessarily exist in a
countable model; that is,
countability is "relative" to a model, and
countable, first-order
models are incomplete....
