Inverse limits with subsets of [ 0 , 1 ] cross [ 0 , 1 ]
نویسندگان
چکیده
The characterization of chainable continua as inverse limits on [0, 1] has resulted in many papers which have contributed to our knowledge of both inverse limits and chainable continua. Quite simple maps on [0, 1] give rise to quite complicated inverse limits. In this paper we begin an investigation of continua that can be represented by inverse limits of closed subsets of the unit square I = [0, 1] × [0, 1]. We show that some of the usual properties of inverse limits are valid in this situation, give numerous examples, and provide conditions under which the inverse limit is a continuum.
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