-
different topologies. For instance, the real line, the
complex plane, and the
Cantor set can be
thought of as the same set with
different topologies. Formally...
- invariably, a
physical bus
topology. Two
basic categories of
network topologies exist,
physical topologies and
logical topologies. The
transmission medium...
- not
generally the
union of
those topologies (the
union of two
topologies need not be a
topology) but
rather the
topology generated by the union.
Every complete...
-
Grothendieck topologies. Conversely,
there are
Grothendieck topologies that do not come from
topological spaces. The term "Grothendieck
topology" has changed...
- a
strong topology is a
topology which is
stronger than some
other "default"
topology. This term is used to
describe different topologies depending on...
-
completely normal Hausdorff space. The
standard topologies on R, Q, Z, and N are the
order topologies. If Y is a
subset of X, X a
totally ordered set...
- In mathematics, weak
topology is an
alternative term for
certain initial topologies,
often on
topological vector spaces or
spaces of
linear operators,...
-
generates the
topology T.
Bases are
useful because many
properties of
topologies can be
reduced to
statements about a base that
generates that
topology—and because...
-
space topology are
relatively rarely used. To summarize, the
three essential topologies on B(H) are the norm, ultrastrong, and
ultraweak topologies. The...
- compact.
Cofinite topology List of
topologies Steen, Lynn Arthur; Seebach, J.
Arthur Jr. (1995) [1978],
Counterexamples in
Topology (Dover
reprint of...
