SpaceWeather.com -- News and information about meteor showers, solar flares, auroras, and near-Earth asteroids: "We've already had one Blue Moon in January 2018, a month bookended by full Moons on the 2nd (02:24 UTC) and 31st (13:27 UTC). It's happening again in March, with full Moons on the 2nd (00:51 UTC) and 31st (12:37 UTC). The last time two Blue Moons occurred in such quick succession was January and March of 1999."
'via Blog this'
Slacks of 24 hours at the beginning of the month and ~12 hours around the end.
Sunday, April 01, 2018
Saturday, March 17, 2018
Immersion (mathematics) - Wikipedia
Immersion (mathematics) - Wikipedia: "For example, the Möbius strip has non-trivial tangent bundle, so it cannot immerse in codimension 0 (in R2), though it embeds in codimension 1 (in R3).
"
'via Blog this'
"
'via Blog this'
Orientability - Wikipedia
Orientability - Wikipedia: " a loop going around one way on the surface can never be continuously deformed (without overlapping itself) to a loop going around the opposite way."
that is homeomorphic to the Möbius strip. Thus, for surfaces, the Möbius strip may be considered the source of all non-orientability.
'via Blog this'
that is homeomorphic to the Möbius strip. Thus, for surfaces, the Möbius strip may be considered the source of all non-orientability.
'via Blog this'
Wednesday, March 07, 2018
Topological group - Wikipedia
Topological group - Wikipedia: "The groups mentioned so far are all Lie groups, meaning that they are smooth manifolds in such a way that the group operations are smooth, not just continuous."
'via Blog this'
'via Blog this'
Tuesday, March 06, 2018
[PDF] Schuller's Geometric Anatomy of Theoretical Physics, Lectures 1-17 - Free Download PDF
[PDF] Schuller's Geometric Anatomy of Theoretical Physics, Lectures 1-17 - Free Download PDF:
{b} is neither open nor closed
Example 5.7. The interval [0, 1] is compact in (R, Ostd). The one-element set containing (−1, 2) is a cover of [0, 1], but it is also a finite subcover and hence [0, 1] is compact from the definition.
It is clear that removing even one element from C will cause C to fail to be an open cover of R. Therefore, there is no finite subcover of C and hence, R is not compact.
{b} is neither open nor closed
Example 5.7. The interval [0, 1] is compact in (R, Ostd). The one-element set containing (−1, 2) is a cover of [0, 1], but it is also a finite subcover and hence [0, 1] is compact from the definition.
It is clear that removing even one element from C will cause C to fail to be an open cover of R. Therefore, there is no finite subcover of C and hence, R is not compact.
Example
4.6
.
Let
M
=
{
a,b,c
}
and let
O
=
{
∅
,
{
a
}
,
{
a,b
}
,
{
a,b,c
}}
. Then
{
a
}
is open
but not closed,
{
b,c
}
is closed but not open, and
{
b
}
is neither open nor close
Example
4.6
.
Let
M
=
{
a,b,c
}
and let
O
=
{
∅
,
{
a
}
,
{
a,b
}
,
{
a,b,c
}}
. Then
{
a
}
is open
but not closed,
{
b,c
}
is closed but not open, and
{
b
}
is neither open nor close
'via Blog this'
Subscribe to:
Posts (Atom)