Here's why ACME means QUALITY in ZERO
VOLUME BOTTLES:
 Acme engineers use our familiar 3dimensions.
Result? You can actually hold an Acme Klein Bottle in your hand. Those
highfalutin' 4dimensional ones can only be held in your mind.
 We select the finest quality genus1
manifolds, so each Acme Klein Bottle includes a builtin handle at no
extra cost.
 With a carefully positioned center
of gravity, your Acme Klein Bottle stands on its own. No external support
needed, nor cumbersome spacetime springhook.
 Microwave safe, batteries not required,
Y2K compliant.
 Our technicians painstakingly adjust
each Acme Klein Bottle for an Euler Characteristic very, very close
to zero.
 With each Klein Bottle, Acme includes
a manifold free of any covering of coherently oriented coordinate neighborhoods.
And an Acme Klein Bottle allows a closed curve /s/ which is such
that a small oriented circle whose center traverses the curve continuously
to arrive at its starting point with its orientation reversed. If this
makes sense, then you simply must own an Acme Klein Bottle.
 Your Acme Klein Bottle is hand crafted
in low expansion borosilicate glass by a team of happy glassblowers,
ceramicists & one gourmet cook. Triple sealed with an oxyhydrogen
torch, annealed, then individually inspected by a bestselling author
and PhD astrophysicist who holds an advanced degree in radiative transfer!
 You can convert your Acme Klein Bottle
into an astonishing amount of energy, over 10^{23} ergs! Enough
to power a small city for years. To get you started, we'll supply the
necessary equation for free.
 Buy an Acme Klein Bottle and a pair
of scissors, then PROVE TO YOUR NEIGHBORS that it has a Betti Number
of 2. They'll be astounded when you make two cuts into the manifold
without dividing the surface into two separate pieces.
 Acme High Performance Klein Bottles
are made on a planet rich in silicon dioxide  we never clearcut rainforests,
stripmine Kentucky towns, or smash oil tankers into arctic shores.
 All manifolds are homogeneous, that
is, every small piece looks like a piece of Euclidean space of the same
dimension. Immersed in 3 dimensions, a Klein bottle's surface must intersect
itself at the nexus, and Acme cleverly uses an elegant transverse puncture.
Inferior 4D Klein Bottles lack this selfintersection feature.
 You can actually fill your Acme Klein
Bottle with colored water! (In Britain, use coloured water) Impress
your friends, astound your professors, and baffle next year's graduating
class!
 Every Acme Klein Bottle comes with
a free topological fundamental group which can be homomorphically mapped
onto the BaumslagSolitar group. Perfect for dorm parties.
 Acme Klein Bottles incorporate
NO UNNECESSARY MAGNETIC MONOPOLES. And our low coefficient of expansion
insures that the bottle's size remains almost invariant with temperature.
 Speaking of invariance ... worried
about Lorentz contractions? No problem with an Acme Klein Bottle! It's
designed to work in EVERY frame of reference (though not necessarily
simultaneously).
 Don't worry if you find some
Cantor dust ... it has zero measure and won't affect your Klein bottle's
high performance.
 Absolutely free from all harmful radio
emissions  guaranteed not to interfere with any broadcasting station,
20 meter sideband transceiver, wifi hotspot, SETI system, or cosmic
ray detector.
 Want to connect geometry with topology?
Check this out: You can integrate the Gaussian curvature of your Acme
Klein Bottle and the result will be exactly 2π times its Euler characteristic.
Is that cool or what? Gauss and Bonnet would be very happy!
 Buy with confidence  your Acme Klein
Bottle comes with a unconditional
guarantee which
includes NO FEWER THAN SEVEN conditions.
 Your money back if not satisfied!
(However, we suspect that we will be quite satisfied with your money)
 Your Acme Klein Bottle's fundamental
group equals the direct product of the integers with the integers modulotwo!
What does this mean? Don't ask me.
 Acme uses no expensive palladium compounds
so there's minimal danger of coldfusion byproducts.
 Your Acme Klein Bottle is transparent
to most forms of visible radiation, yet blocks harmful extreme ultraviolet
rays.
 It's rustproof, even in Wisconsin.
 Runofthemill Klein Bottles are
homeomorphic to a sphere with two crosscaps. Thanks to the Acme's exclusive
transverse puncture, Acme Klein Bottles are homeomorphic to a disc
with two crosscaps. Especially useful during the extreme weather conditions
encountered in the palagonite plains around Utopia Planitia.
 If you often travel through a nonorientable
wormholes, you'll be comforted to know that your Acme Klein Bottle is
a reasonable analog to most Alice universes.
 According to the Firesign Theater,
you can use these to trap Mars flies.
 Ask about our special BanachTarski
TWOFORONE SALE!
 Acme Klein Bottles are designed using
advanced numerical models done on a high speed Curta calculator.
 We employ skilled craftsfolk from
around the Earth, including the USA and the People's Republic of Berkeley.
We also employ unskilled workers, but they mainly spend their time surfing
the web.
 Tired of point set topology and semimetric
space? Imagine the look on your instructor's face when you pop out an
Acme Klein Bottle!
 Acme's glassblowers select from a
flavorful palatte of borosilicate glass  including such brands as
Pyrex, Kimax, Simax, Bomex  so you can be sure to receive exactly
what they choose. With its Poisson ratio of 0.2, you won't be tempted
to crush your bottle to save space. Just as nice  the glass has a
bulk density of 2.23 gm/cm^{3}. (Of course, a Klein Bottle's
density is undefined since it has zero volume.)
 Lifetime guarantee  we guarantee
that you will live your full lifetime!
 CERTIFIED CHIRALITY FREE! For
every LeftHanded Moebius Loop within our Klein Bottle, we include an
equal and opposite handed RightHanded Moebius Loop.
 At any time  day or night  you
can easily check on the Euler Characteristic of your Acme Klein Bottle.
Just add the number of vertices to the number of faces, then subtract
the number of edges. So simple, even a grad student can do it!
 For the ULTIMATE IN DIMENSIONAL
STABILITY, we make each Klein Bottle from a special blend of
borosilicate glass ... it expands a mere 0.000326% per degree C! So
your Acme Klein Bottle will shrink only a few microns when you
trek from Nogales to Nome.
 No reason to worry about the incorrect
number of perforations. Acme's Department of Holes and Handles inspects
each Klein Bottle to make sure it contains exactly one hole.
 Solve Hodge's conjecture! It's one
of the most baffling unsolved problems in mathematics, involving the
relationship the algebraic topology of nonsingular conplex algebraic
varieties and subvarieties. You  Yes YOU  can be the first
to Solve Hodge's Conjecture ... simply purchase a dozen Acme Klein Bottles
and then just develop a generalized theory for the sums of Poincaré
Duals of homology classes of subvarieties. You'll win the Fields Medal
and the Clay Millennium Prize ... get invited to colloquia which
often offer FREE COOKIES!
 Travellers in space and time will
especially appreciate that Acme's differential geometry technicians
carefully tune each Acme Klein Bottle until its Systolic ratio is no
more than π/√ 8
 BREAKING NEWS! Acme's Klein bottles are now parallelizable! Buy dozens
of 'em and you can supply your own choice of Lie Groups. Good luck drawing
a vector field on 'em.
 Your manifold is shipped to you in
a box made from genuine organic materials, specially
padded to reduce shock and vibration. Ecologically friendly packaging
can be recycled.
 We do not use a turboencabulator
to manufacture our Acme Klein Bottles.
 Remember the four color theorem? Well,
since its chromatic number is 6, maps drawn on an Acme Klein Bottle
need six colors. Unpack those Crayolas and prove it to yourself! (In
fact, the Klein Bottle is the only exception to the Heawood
Conjecture, so don't go into the map printing business.)
 You aren't supporting some uncaring
multinational monolith  Acme's parent division supports every good
cause and is on the side of truth, justice, and world peace.
 Acme donates all of its nonexistent
profits to a college fund for the owner's children.
