Mapping Theorems for Rigid Continua and Their Inverse Limits

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.…”

“…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. There are many rigid continua or continua that are not 0-rigid that are constructed using Cook continua, see [2,6,10], where more references may be found. For example, in [2], Cook continua are used to construct stars, paths, and cycles of Cook continua.…”

“…There are many rigid continua or continua that are not 0-rigid that are constructed using Cook continua, see [2,6,10], where more references may be found. For example, in [2], Cook continua are used to construct stars, paths, and cycles of Cook continua. They are all examples of continua that are not 0-rigid.…”

“…They are all examples of continua that are not 0-rigid. It was shown in [2] that for each positive integer m, X such that 1. X is 1 m -rigid, and 2. for any inverse sequence {X , f n } with surjective continuous bonding functions f n the inverse limit lim ← − {X , f n } is homeomorphic to X .…”

“…Problem 1 [2,Problem 5.7] Find all non-degenerate continua X such that 1. degrig(X ) = ∞, 2. lim ← − {X , f n } is homeomorphic to X for any sequence ( f n ) of continuous surjections f n : X → X.…”