Last Updated：2025/12/30
Sentence
A
Möbius
strip
is
a
fiber
bundle
which
looks
locally
(i.e.,
over
a
connected
proper
subset
of
its
base
space)
like
the
corresponding
part
of
a
cylinder
S¹⨯[0,1]
(a
Möbius
strip
and
a
cylinder
have
isomorphic
base
spaces).
A
Klein
bottle
is
a
fiber
bundle
which
looks
locally
like
the
corresponding
part
of
a
torus
S¹⨯S¹
(again
they
could
be
thought
of
as
sharing
the
same
base
space
S¹;
cutting
out
even
a
single
point
of
that
base
space
makes
the
cut
Klein
bottle
isomorphic
to
the
cut
torus).
Quizzes for review
A Möbius strip is a fiber bundle which looks locally (i.e., over a connected proper subset of its base space) like the corresponding part of a cylinder S¹⨯0,1. A Klein bottle is a fiber bundle which looks locally like the corresponding part of a torus S¹⨯S¹ (again they could be thought of as sharing the same base space S¹; cutting out even a single point of that base space makes the cut Klein bottle isomorphic to the cut torus).
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