# Fractals everywhere by Barnsley M.F.

By Barnsley M.F.

Best topology books

Modern Geometry: Introduction to Homology Theory Pt. 3: Methods and Applications

During the last fifteen years, the geometrical and topological equipment of the idea of manifolds have assumed a primary position within the so much complex components of natural and utilized arithmetic in addition to theoretical physics. the 3 volumes of "Modern Geometry - tools and purposes" include a concrete exposition of those equipment including their major purposes in arithmetic and physics.

Borel Liftings of Borel Sets: Some Decidable and Undecidable Statements

One of many goals of this paintings is to enquire a few average homes of Borel units that are undecidable in $ZFC$. The authors' start line is the next easy, even though non-trivial consequence: reflect on $X \subset 2omega\times2omega$, set $Y=\pi(X)$, the place $\pi$ denotes the canonical projection of $2omega\times2omega$ onto the 1st issue, and think that $(\star)$ : ""Any compact subset of $Y$ is the projection of a few compact subset of $X$"".