- &4\leftrightarrow 8,&\ldots \end{matrix}}}
Every countably infinite set is
countable, and
every infinite countable set is
countably infinite. Furthermore, any subset...
- non-increasing
functions of t , {\displaystyle t,} so both of them have at most
countably many
discontinuities and thus they are
continuous almost everywhere, relative...
- mathematics, the term
countably generated can have
several meanings: An
algebraic structure (group, module, algebra)
having countably many generators, see...
- topology, a second-
countable space, also
called a
completely separable space, is a
topological space whose topology has a
countable base. More explicitly...
- a
branch of mathematics, a first-
countable space is a
topological space satisfying the "first
axiom of
countability". Specifically, a
space X {\displaystyle...
- mathematics, an
axiom of
countability is a
property of
certain mathematical objects that ****erts the
existence of a
countable set with
certain properties...
-
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:...
- topology) is an
example of a
countably compact space that is not compact.
Every compact space is
countably compact. A
countably compact space is
compact if...
- connected,
locally connected and pseudocompact, but
neither weakly countably compact nor
countably metacompact,
hence not compact.
Uncountable set: On any uncountable...
-
union of
countably many
countable sets is
countable.
These statements are not equivalent: Cohen's
First Model supplies an
example where countable unions...
