This paper combines two aspects in the construction of knowledge spaces. The first is to utilize a partial order of skills which belong to a given domain of knowledge to find items or problems which finally constitute a knowledge space or a learning space. Secondly the orders of skills of different (related) areas are coalesced by well known order operations to construct larger spaces.

In the first part a so called basic set representation of an order is utilized to considerably simplify the construction of knowledge spaces.

In the second part the techniques to “add” and “multiply” orders are applied to given orders resulting in new orders to which the set representation theory of the first part is applied. Properties of the building blocks are identified which can be transferred to the combination and yield properties of the final knowledge space which make their handling a bit more convenient. In particular, places which proved useful in the construction of the first part are identified when these order operations are utilized.

本文结合了知识空间建设的两个方面。首先是利用属于给定知识领域的部分技能顺序来找到最终构成知识空间或学习空间的项目或问题。其次，不同（相关）领域的技能顺序通过众所周知的顺序操作合并在一起，以构造更大的空间。

在第一部分中，使用所谓的订单基本集表示形式来显着简化知识空间的构造。

在第二部分中，将“加”和“乘”定单的技术应用于给定的定单，从而产生新的定单，将第一部分的集合表示理论应用于该定单。确定了构建基块的属性，这些属性可以转移到最终知识空间的组合中，并产生最终知识空间的属性，从而使它们的处理更加方便。特别地，当利用这些订购操作时，将确定在第一部分的构造中被证明有用的地方。