Cleavability in Ordered Spaces - Semantic Scholar
Cleavability in Ordered Spaces Harold Bennett and Robert Byerly Texas Tech University, Lubbock, TX 79409
David Lutzer College of William and Mary, Williamsburg, VA 23187 Abstract. In this paper we study the role of cleavability and divisibility in the topology of generalized ordered (GO-)spaces. We characterize cleavability of a GOspace over the class of metrizable spaces, and over the spaces of irrational and rational numbers. We present a series of examples related to characterizations of cleavability over separable metric spaces and over the space of real numbers. Keywords: cleavability, linearly ordered space, generalized ordered space, divisibility MR Subject Classifications: (Primary) 54F05, 06A05; (Secondary) 06B30,06F30
1. Introduction Recall that a linearly ordered topological space (LOTS) is a linearly ordered set equiped with the usual open-interval topology of the given order. By a generalized ordered space (GO-space) we mean a triple (X, T ,
David Lutzer College of William and Mary, Williamsburg, VA 23187 Abstract. In this paper we study the role of cleavability and divisibility in the topology of generalized ordered (GO-)spaces. We characterize cleavability of a GOspace over the class of metrizable spaces, and over the spaces of irrational and rational numbers. We present a series of examples related to characterizations of cleavability over separable metric spaces and over the space of real numbers. Keywords: cleavability, linearly ordered space, generalized ordered space, divisibility MR Subject Classifications: (Primary) 54F05, 06A05; (Secondary) 06B30,06F30
1. Introduction Recall that a linearly ordered topological space (LOTS) is a linearly ordered set equiped with the usual open-interval topology of the given order. By a generalized ordered space (GO-space) we mean a triple (X, T ,
