A fixed-point theorem

Introduction. The purpose of this note is to sharpen a recent result of G. E. Schweigert [4]. It will be shown that the condition of semi local-connectedness may be dropped. However, if this is strengthened to local-connectedness, then the conclusion asserts the existence of a fixed point. Further, though perhaps of less interest, it is shown that separability is not necessary. In a second section we give a somewhat more abstract version which is valid for certain partially ordered topological spaces. So far as is known this is the first result of this type to appear in the literature.