Topological Lion Hunting
According to the Invariance of Domain Theorem (Brouwer), we may assume
without loss of generality that the hunt takes place in the Sahara desert.
- If the desert is a separable space, there is a sequence converging
to any lion. Choose one such and approach stealthily along it, bearing
If the desert is not separable, there is a net converging to the lion. Use
- Topologize the desert with the leonine topology, in which a
set is closed if and only if it contains no lions, or is the whole desert.
Then the set of lions is dense. Place an open cage in the desert,
and shut the door quickly.
- A lion has at least the connectivity of a torus. Embed the desert in
4-space, and deform it so as to knot the lion. This renders it helpless, and
- A lion is a topological manifold with boundary. Any such can be
- Regard a lion as an orientable 3-manifold. It can be made
via a sequence of surgeries. Contract the lion to a circus.
- A lion is a cross-section of the sheaf of germs of lions on the
desert. Changing the topology of the desert to the discrete topology, the
stalks decompose into their component germs and infect the lion. This makes
the lion ill, hence helpless.
- Lions are hairy, so we regard them as made up of fibers, hence as
fibrations. Construct a Moore-Postnikov decomposition. A decomposed lion
is dead, in need of burial.
- A lion has the homotopy type of a 1-dimensional complex, hence is a
K(G,1). If G is not abelian, then the lion is not a member
of the International Commutist Conspiracy, thus friendly. If G is
abelian, then the lion has the homotopy type of the loop space of
K(G,2). Hire a stunt pilot to loop the loops, thereby thoroughly
entangling the lion.