Rigidity of hyperspaces

Meshed continua have unique second and third symmetric products

“…We use, adapt and generalize results that have been published in the area of uniqueness of hyperspaces, the more related ones can be found in [1][2][3][4]6,7] and [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23].…”

“…We recall that, as in [10], a wire in a continuum X is a subset α of X such that α is homeomorphic to one of the spaces (0, 1), [0, 1), [0, 1] or the unit circle S 1 in the Euclidean plane, and α is a component of an open subset of X. Given a continuum X, let W (X) = {α ⊂ X: α is a wire in X}.…”

Uncountable Family of 0-Rigid Continua that are Homeomorphic to Their Inverse Limits

“…The rigidity of topological spaces has been studied in various ways by different authors, e.g., [1][2][3][4][5][6][7][8][10][11][12]. Cook continua are basic examples of non-degenerate continua that are rigid, and therefore, they play an important role in the study of rigid continua, also in continuum theory and dynamical systems in general.…”