. .. Because Acme makes the finest manifolds!

Here's why ACME means QUALITY in ZERO VOLUME BOTTLES: Acme engineers use our familiar 3-dimensions. Result? You can actually hold an Acme Klein Bottle in your hand. Those highfalutin' 4-dimensional ones can only be held in your mind.

We select the finest quality genus-1 manifolds, so each Acme Klein Bottle includes a built-in 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 space-time 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 oxy-hydrogen torch, annealed, then individually inspected by a best-selling 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 4-D Klein Bottles lack this self-intersection feature.

You can actually fill your Acme Klein Bottle with colored water! (In Canada, Britain, New Zealand, and Oz, 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 Baumslag-Solitar group. Perfect for dorm parties.

Acme Klein Bottle s 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 modulo-two! What does this mean? Don't ask me.

Acme uses no expensive palladium compounds so there's minimal danger of cold-fusion 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.

Run-of-the-mill 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.

If you believe in the axiom of choice, ask about our special Banach-Tarski TWO-FOR-ONE 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 semi-metric 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 Left-Handed Moebius Loop within our Klein Bottle, we include an equal and opposite handed Right-Handed 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!

F or 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 non-singular 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 Poincar� 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.

Our glass Klein bottles are certified DHMO FREE - they contain no dangerous Dihydrogen Monoxide

What dormatory is complete without an genuite operating Klein bottle? After you've received and used it, you'll ask, "How did I ever get along without a Klein bottle?" Klein bottles can be shared with the whole family.

Your manifold is shipped to you in a box made from genuine organic materials, spe cially padded to reduce shock and vibration. Ecologically friendly packaging can be recycled. As a special feature for our valued (and non-valued) customers, we personalize the package with YOUR VERY OWN name and address.

As a special feature for our valued (and non-valued) customers, we personalize the package with YOUR VERY OWN name and address. We do not use a turbo-encabulator 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.