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Join (Spaces)

Let $X$ and $Y$ be Topological Spaces. Then their join is the factor space

X*Y =(X\times Y\times I)/\sim{},

where $\sim$ is the Equivalence Relation

(x,y,t) \sim (x',y',t') \Leftrightarrow \cases{
t=t'=0 {\rm...
\hfill {\rm or}\hfill\cr
t=t'=1 {\rm\ and\ } y=y.\cr}

See also Cone (Space), Suspension


Rolfsen, D. Knots and Links. Wilmington, DE: Publish or Perish Press, p. 6, 1976.

© 1996-9 Eric W. Weisstein