-
topology is
initial or free, the
indiscrete topology is
final or cofree:
every function from a
topological space to an
indiscrete space is continuous, etc. Cylinder...
- are the
empty set and the
entire space. Such
spaces are
commonly called indiscrete, anti-discrete,
concrete or codiscrete. Intuitively, this has the consequence...
- an
indiscrete category is a
category in
which there is
exactly one
morphism between any two objects.
Every class X
gives rise to an
indiscrete category...
- X = { 1 , 2 , 3 , 4 } , {\displaystyle X=\{1,2,3,4\},} the
trivial or
indiscrete topology on X {\displaystyle X} is the
family τ = { { } , { 1 , 2 , 3...
-
sober space from its ****ociated site.
However simple examples such as the
indiscrete topological space show that not all
topological spaces can be expressed...
- and a
right adjoint I : Set → Top
which equips a
given set with the
indiscrete topology. Both of
these functors are, in fact,
right inverses to U (meaning...
-
classes of
countable Toronto spaces, namely: the
discrete topology, the
indiscrete topology, the
cofinite topology and the
upper and
lower topologies on...
- no
subset can be open
except the
space itself and the
empty set (the
indiscrete topology). In practice, however, open sets are
usually chosen to provide...
- ISBN 9780199602957. Rota, Gian-Carlo (1997). Palombi,
Fabrizio (ed.).
Indiscrete Thoughts. Boston, MA: Birkhäuser. doi:10.1007/978-0-8176-4781-0. ISBN 978-0-8176-4781-0...
- is
closed (and also open),
every set is
equal to its closure. In any
indiscrete space X , {\displaystyle X,}
since the only
closed sets are the empty...
