Join (topology)

In Topology , a field of Mathematics , the join of two Topological Space s ''A'' and ''B'' is defined to be the Quotient Space
:

A 	imes B 	imes I / R, \,

where ''I'' is the Interval 1 and ''R'' is the relation defined by
:

(a, b_1, 0) \sim (a, b_2, 0) \quad\mbox{for all } a \in A \mbox{ and } b_1,b_2 \in B,

(a_1, b, 1) \sim (a_2, b, 1) \quad\mbox{for all } a_1,a_2 \in A \mbox{ and } b \in B.

In effect, one is collapsing

A	imes B	imes \{0\}

A

and

A	imes B	imes \{1\}

B

.

SEE ALSO

REFERENCES

Hatcher, Allen , ''Algebraic topology.'' Cambridge University Press, Cambridge, 2002. xii+544 pp. ISBN 052179160X and ISBN 0521795400

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