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Some Properties Of Hereditarily Indecomposable Chainable Continua, Thomas John Kacvinsky

Masters Theses

"In 1920, B. Knaster and C. Kuratowski raised the question of whether each homogeneous plane continuum is a simple closed curve. In 1921, S. Mazurkiewicz raised the question of whether each subcontinuum of Euclidean n-space which is homeomorphic to each of its subcontinua is necessarily an arc. In that same year, B. Knaster and C. Kuratowski raised the question of whether there exists a nondegenerate hereditarily indecomposable continuum.

The third question was answered in the affirmative in 1922 by B. Knaster, when he constructed a nondegenerate hereditarily indecomposable subcontinuum of the plane.

The second question was answered in 1947 by …