empty
The exclamation mark(
), can be also used as a separate quantification symbol, so
, where
. E.g. it can be safely used in the replacement axiom, instead of
.
A topology is exactly an element of the proper class
, which is defined the following way:
. The underlaying set
can be unambiguously reconstructed from the topology, because
. Propeties
and
are simple theorems, which follow from the right part of the conjunction in the definion of
.