Projections of a learning space

TL;DR

This paper explores how projecting a learning space onto subsets of its domain results in smaller, consistent learning spaces, aiding in managing large learning spaces effectively.

Contribution

It provides a direct proof that projections and partitions of learning spaces preserve their structure, facilitating the parsing of large learning spaces.

Findings

Projections of learning spaces are themselves learning spaces.

Partitions of the domain induce smaller learning spaces.

These properties help in managing large learning spaces.

Abstract

Any subset Q' of the domain Q of a learning space defines a projection of that learning space on Q' which is itself a learning space consistent with the original one. Moreover, such a construction defines a partition of Q having each of its classes defining a learning space also consistent with the original learning space. We give a direct proof of these facts which are instrumental in parsing large learning spaces.