Last Updated：2025/12/20
Sentence
To
get
an
intuitive
feeling
for
the
characteristics
of
H'-spaces,
it
is
instructive
to
consider
an
important
class
of
such
spaces,
the
suspensions.
The
suspension
of
an
arbitrary
topological
space
Y
is
defined
to
be
the
quotient
space
of
Y⨯I
where
Y⨯0
is
identified
to
one
point
and
Y⨯1
is
identified
to
another
point.
For
example,
the
suspension
of
a
circle
is
a
cylinder
with
the
two
ends
collapsed
into
one
point
each;
in
other
words,
a
space
homeomorphic
to
a
sphere.
Quizzes for review
To get an intuitive feeling for the characteristics of H'-spaces, it is instructive to consider an important class of such spaces, the suspensions. The suspension of an arbitrary topological space Y is defined to be the quotient space of Y⨯I where Y⨯0 is identified to one point and Y⨯1 is identified to another point. For example, the suspension of a circle is a cylinder with the two ends collapsed into one point each; in other words, a space homeomorphic to a sphere.
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