Donovan

Virginiaz said:

Topology. Please discuss.

What would you like to know about it ? Are you considering
studying it ?

Topologists are interested in studying topological
invariants of various objects. That is, they look at
properties that are independent of things like bending and
stretching. If you can map one object to another with a 1-1
mapping that is continuous and has a continuous inverse,
then to a topologist, they are the same thing (if two
objects can be mapped such a way, they are homoemorphic, or
one could simply say, topologically equivalent).

So the topologist looks for algebraic and geometric
properties that apply across a homoemorphism class. For
example, Euler characteristic of a surface is topology
invariant (so it's 2 for any polygon but 0 for a torus)

Some of these may involve a certain amount of geometry. For
example, knot theory looks at the space around the knot. The
geometry of the embedding is important, even though the knot
is always topologically a surface (though the way it is
embedded varies)

Another toplogical invariant is the number of connected
components ("connected" means what you think it means. A
connected component is a maximal connected subset)

There are actually algebraic invariants of topological
objects. For example, one could define a formal sum with
integer coefficients assigned to each connected component,
(x1 C1,x2 C2,x3 C3) where C1, ... , C3 are components and x1
are coefficients. Then one can define an operation + by:
(x1,x2,x3) + (y1,y2,y3) = (x1+y1,x2+y2,x3+y3) This algebraic
structure is a topological invariant (a "homology group"
actually). Most of the work I did involved exploring
algebraic invariants of topological objects.

HTH,
--
Donovan Rebbechi pegasus.rutgers.edu~elflordOpen ↗

WTF did he say???

Donovan Rebbechi <[email hidden]> wrote in message
news:<[email hidden]>...

Quoted message said:

Virginiaz said:

Topology. Please discuss.

What would you like to know about it ? Are you considering
studying it ?

Topologists are interested in studying topological
invariants of various objects. That is, <snip gibberish

Donovan Rebbechi said:

Virginiaz said:

Topology. Please discuss.

What would you like to know about it ? Are you considering
studying it ?

[snip]

Group Theory and Ring Theory was tough enough for me, so I
decided to skip Topology all together and took Diff EQ
instead. But that was more than two decades ago.

Easy enough to understand, but more importantly, how is this
going to help to make the perfect cup of expresso?

Donovan Rebbechi said:

Virginiaz said:

Topology. Please discuss.

What would you like to know about it ? Are you considering
studying it ?

Topologists are interested in studying topological
invariants of various objects. That is, they look at
properties that are independent of things like bending and
stretching. If you can map one object to another with a
1-1 mapping that is continuous and has a continuous
inverse, then to a topologist, they are the same thing (if
two objects can be mapped such a way, they are
homoemorphic, or one could simply say, topologically
equivalent).

So the topologist looks for algebraic and geometric
properties that apply across a homoemorphism class. For
example, Euler characteristic of a surface is topology
invariant (so it's 2 for any polygon but 0 for a torus)

Some of these may involve a certain amount of geometry.
For example, knot theory looks at the space around the
knot. The geometry of the embedding is important, even
though the knot is always topologically a surface (though
the way it is embedded varies)

Another toplogical invariant is the number of connected
components ("connected" means what you think it means. A
connected component is a maximal connected subset)

There are actually algebraic invariants of topological
objects. For example, one could define a formal sum with
integer coefficients assigned to each connected component,
(x1 C1,x2 C2,x3 C3) where C1, ... , C3 are components and
x1 are coefficients. Then one can define an operation +
by: (x1,x2,x3) + (y1,y2,y3) = (x1+y1,x2+y2,x3+y3) This
algebraic structure is a topological invariant (a
"homology group" actually). Most of the work I did
involved exploring algebraic invariants of topological
objects.

HTH,

"Donovan Rebbechi" <[email hidden]> wrote in message
"]news:[email hidden]...

Quoted message said:

On 2004-07-08, Virginiaz <[email hidden]> wrote:

Quoted message said:

Quoted message said:

Topology. Please discuss.

Quoted message said:

Topologists are interested in studying topological
invariants of various objects.

Fascinating.

I never fail to be surprised by the directions into which
'science' can delve in the most esoteric, baffling and
completely pointless manner. Sure, I know you have to go
climb distant hills to see if the view is worth seeing, but
common sense suggests that we should climb the hills that
*look* like they might provide interesting perspectives
before we wander up each and every lump that presents itself
before us. Our time on this earth is finite, and we are
obliged to use this time in the most beneficial manner for
ourselves and our species.

Clearly, you have a brain well suited to dealing with the
minutia of a subject and you revel in the intellectual
satisfaction thus provided. But I'm forced to ask why a
young, capable, and articulate individual in the prime of
his working life is wasting his time on Usenet partaking
in the most mind-numbingly boring discussions on almost
every contentions aspect of running whilst at the same
time studying a subject that can only - with the best
will in the world - be described as 'of pheripheral
benefit' to humanity?

On Thu, 8 Jul 2004 22:47:52 +0000 (UTC), Donovan Rebbechi <[email hidden]>

Quoted message said:

Virginiaz said:

Topology. Please discuss.

What would you like to know about it ? Are you considering
studying it ?

Topologists are interested in studying topological
invariants of various objects. That is, they look at
properties that are independent of things like bending and
stretching. If you can map one object to another with a 1-1
mapping that is continuous and has a continuous inverse,
then to a topologist, they are the same thing (if two
objects can be mapped such a way, they are homoemorphic, or
one could simply say, topologically equivalent).
. . .

Brother in law is a math kinda guy, so I have learned: the
doughnut is topologically equivalent to the coffee mug! :-)

--
Daniel
[email hidden]

Dangling said:

WTF did he say???

Never mind, you don't need to know this stuff to run (or for
that matter, to troll)

Cheers,
--
Donovan Rebbechi pegasus.rutgers.edu~elflordOpen ↗

But how's learning how to make a perfect cup of expresso(?)
going to help with refueling a Sukhoi Su-30?

Bumper said:

Easy enough to understand, but more importantly, how is
this going to help to make the perfect cup of expresso?

Donovan Rebbechi <[email hidden]> wrote:

....

"Bumper" <[email hidden]> wrote in message

Quoted message said:

Easy enough to understand, but more importantly, how is
this going to help to make the perfect cup of expresso?

It's spelled espresso - I'm not trying to be a smartass or
anything, its almost never spelled right, even on some signs
in coffee stores! :-)

cheers,
--
David (in Hamilton, ON) www.allfalldown.org
www.absolutelyaccurate.com

Bumper said:

Easy enough to understand, but more importantly, how is
this going to help to make the perfect cup of expresso?

Take up grad school and get an espresso machine. By the time
you graduate, you'll be pretty good at making the stuff (I
speak from experience).

Cheers,
--
Donovan Rebbechi pegasus.rutgers.edu~elflordOpen ↗

np426z said:

Clearly, you have a brain well suited to dealing with the
minutia of a subject and you revel in the intellectual
satisfaction thus provided. But I'm forced to ask why a
young, capable, and articulate individual in the prime of
his working life is wasting his time on Usenet partaking
in the most mind-numbingly boring discussions on almost
every contentions aspect of running

I don't know. Why do we do it ? (-;

Quoted message said:

whilst at the same time studying a subject that can only -
with the best will in the world - be described as 'of
pheripheral benefit' to humanity?

I work in a psychology department now. But interestingly
enough, I see more and more advanced math making its way
into that field.

Cheers,
--
Donovan Rebbechi pegasus.rutgers.edu~elflordOpen ↗

Daniel said:

Donovan Rebbechi said:

Virginiaz said:

Topology. Please discuss.

What would you like to know about it ? Are you considering
studying it ?

Topologists are interested in studying topological
invariants of various objects. That is, they look at
properties that are independent of things like bending and
stretching. If you can map one object to another with a
1-1 mapping that is continuous and has a continuous
inverse, then to a topologist, they are the same thing (if
two objects can be mapped such a way, they are
homoemorphic, or one could simply say, topologically
equivalent).
. . .

Brother in law is a math kinda guy, so I have learned:
the doughnut is topologically equivalent to the coffee
mug! :-)

Yep. So it won't make a barista of you, but at least you'll
always have a doughnut with your coffee.

Cheers,
--
Donovan Rebbechi pegasus.rutgers.edu~elflordOpen ↗

Quoted message said:

It's spelled espresso - I'm not trying to be a smartass or anything,
its almost never spelled right, even on some signs in coffee stores! :-)

I was in a coffee shop in Albuquerque (the Double Rainbow,
IIRC) where the employees' shirts said on the back, "There
is no X in espresso."

--
Brian P. Baresch Fort Worth, Texas, USA Professional editing
and proofreading

If you're going through hell, keep going. --Winston
Churchill

Donovan Rebbechi <[email hidden]> wrote in message news:<[email hidden]>...

Quoted message said:

Dangling said:

WTF did he say???

Never mind, you don't need to know this stuff to run (or
for that matter, to troll)

Cheers,

Oh good, as long as I'm still good at one of the above, I'm
satisfied.

Brian Baresch said:

Quoted message said:

It's spelled espresso - I'm not trying to be a smartass or
anything, its almost never spelled right, even on some
signs in coffee stores! :-)

I was in a coffee shop in Albuquerque (the Double Rainbow,
IIRC) where the employees' shirts said on the back, "There
is no X in espresso."

That's why I drink milk - even *I* can spell it 😉

Dot

I stand corrected, but considering:

1. the time at which I posted,
2. the fact that I can't spell & my newsgroup client doesn't
have a spell checker, and
3. it (espresso) is not my favorite coffee drink
(apparently the real joy of making espresso is in
getting anything tastier than a brew from old gym socks
while forcing steam through a substance that was just
seconds shy of being charcoal-and there is hardly any
caffeine in this liquid!)

The purpose of my post was a gentle tweak of our resident
renaissance man, Donovan, who apparently is just as
comfortable discussing coffee or computers as he is running,
although I suspect he enjoys running more than either of the
preceding two subjects. And now that we learn he is hanging
around the Psych department these days I'm guessing next
he'll be giving Ozzie a run for the therapy side of
rec.running.

Anyway he solved my treadmill problems with a single post so
I will always be indebted to him for that, however, I am
still left wanting to steal his "Cheers" but I suspect that
would be a tad too obvious.

SwStudio said:

"Bumper" <[email hidden]> wrote in message

Quoted message said:

Easy enough to understand, but more importantly, how is
this going to help to make the perfect cup of expresso?

It's spelled espresso - I'm not trying to be a smartass or
anything, its almost never spelled right, even on some
signs in coffee stores! :-)

cheers,