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In: Advanced Math

Take the smallest cellular structure forthe circle X = S1 consisting of a single 0-cell and...

Take the smallest cellular structure forthe circle X = S1 consisting
of a single 0-cell and a single 1-cell. Let Y be the same circle with two 0-cells and two
1-cells with the ends attached to the two different 0-cells. Count (in particular, describe)
all possible (up to homotopy) cellular maps X → Y and Y → X

question related to Topological data analysis 2

Take the smallest cellular structure forthe circle X = S1 consisting
of a single 0-cell and a single 1-cell. Let Y be the same circle with two 0-cells and two
1-cells with the ends attached to the two different 0-cells. Count (in particular, describe)
all possible (up to homotopy) cellular maps X → Y and Y → X

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