id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ijassa-1958	Klimov, Petr; Sengupta, Richik	On the Compatibility of Metric and Linear Order	2025	10	.pdf	application/pdf	4890	262	72	At the same time, only degenerate finite metric spaces (consisting of no more than 3 points), discrete metric spaces, and R fit the conditions for compatibility with some order. In particular, we show that although on all of Rn no order is compatible with the metric, in any normed space one can introduce non-trivial metric subspaces compatible with some order (in the case of infinite-dimensional normed spaces, this subspace can be constructed to be non-embeddable in any finite-dimensional subspace) Keywords: ordered metric spaces, metric spaces, linear order.	cache/ijassa-1958.pdf	txt/ijassa-1958.txt