Solving Two Problems in General Topology Via Types

In the paper we show, based on two problems in general topology (Kuratowski closure-complement and Isomichi’s classification of condensed subsets), how typed objects can be used instead of untyped text to better represent mathematical content understandable both for human and computer checker. We present mechanism of attributes and clusters reimplemented in Mizar fairly recently to fit authors’ expectations. The problem of knowledge reusability which is crucial if we develop a large unified repository of mathematical facts, is also addressed.