I was trying to prove that the set consisting of the union of the circles $\{\langle x,y\rangle\mid(x-10)^2 +y^2 = 1\}$, $\{\langle x,y\rangle\mid(x+10)^2 +y^2 = 1\}$ and line segment $\{\langle x, 0\rangle\mid x\in[-9,9]\}$, is homotopy equivalent to the wedge sum of two circles.To do so I tried to start from the wedge sum of two bigger circles and deformation retract them to the set given , but I couldn't do it , and also I tried to collapse the line to a point then move one of the circles to meet the other , but this doesn't seem to be right, can anyone help me please?
2026-04-02 12:22:28.1775132548
A homotopy equivalence between two sets
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