A common generalization of metric, ultrametric and topological fixed point theorems

作者：Kuhlmann Katarzyna^*; Kuhlmann Franz Viktor

来源：Forum Mathematicum, 2015, 27(1): 303-327.

DOI：10.1515/forum-2012-0060

• Fixed point theorem
• attractor theorem
• metric space
• ultrametric space
• ordered abelian group
• ordered field

We present a general fixed point theorem which can he seen as the quintessence of the principles of proof for Banach's fixed point theorem, ultrametric and certain topological fixed point theorems. It works in a minimal setting, not involving any metrics. We demonstrate its applications to the metric, ultrametric and topological cases, and to ordered abelian groups and fields.

• 出版日期2015-1
• 单位Saskatoon; Saskatchewan