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Inverse limits with set valued functions

Van C. Nall

Open publisher page 38 citations

Abstract

Abstract. We begin to answer the question of which continua can be home-omorphic to an inverse limit with a single upper semi-continuous bonding map from [0, 1] to 2[0,1]. Several continua including [0, 1] × [0, 1] and all com-pact manifolds with dimension greater than one cannot be homeomorphic to such an inverse limit. It is also shown that if the upper semi-continuous bonding maps have only zero dimensional point values, then the dimension of the inverse limit does not exceed the dimension of the factor spaces. 1.

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What this paper is about

Abstract. We begin to answer the question of which continua can be home-omorphic to an inverse limit with a single upper semi-continuous bonding map from [0, 1] to 2[0,1]. Several continua including [0, 1] × [0, 1] and all com-pact manifolds with dimension greater than one cannot be homeomorphic to such an inverse limit. It is also shown that if the upper semi-continuous bonding maps have only zero dimensional point values, then the dimension of the inverse limit does not exceed the dimension of the factor spaces. 1.

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Available abstract

Abstract. We begin to answer the question of which continua can be home-omorphic to an inverse limit with a single upper semi-continuous bonding map from [0, 1] to 2[0,1]. Several continua including [0, 1] × [0, 1] and all com-pact manifolds with dimension greater than one cannot be homeomorphic to such an inverse limit. It is also shown that if the upper semi-continuous bonding maps have only zero dimensional point values, then the dimension of the inverse limit does not exceed the dimension of the factor spaces. 1.

Key concepts: Mathematics, Inverse limit, Inverse, Limit (mathematics), Dimension (graph theory), Pure mathematics, Set (abstract data type), Zero (linguistics)

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