1 Introduction

2 Mathematical Background

2.1 Definition. Bijective Functions and Isomorphisms

2.2 Definition. Metric or Distance Function

2.3 Definition. Open Ball

2.4 Definition. Open Set vs. Closed Set

2.5 Definition. Boundary, Interior, Regular Sets

2.6 Definition. Topology and Topological Space

2.7 Definition. Neighborhood

2.8 Definition. Neighborhood Topology

2.9 Definition. Disks and Half-disks 82 and S1

2.10 Definition. 2-Manifold in R3

2.11 Definition. 2-Manifold with Border in R3

2.12 Definition. 1-Manifold in R3

2.13 Definition. 1-Manifold with Border in R3

2.14 Examples of Non-manifold Topologies

2.15 Definition. Connected Set in R3

3 B-Reps

3.1 Solid (BODY) in R3

3.2 LUMP in R3

3.3 SHELL

3.4 FACE

3.5 LOOP

3.6 EDGE

3.7 VERTEX

3.8 Example. Pre-Columbian Shape

3.9 Examples Non-Manifold

3.10 Example. Manifold Preservation in Parametric CAD

3.10.1 Questions on Boundary - Representation

3.11 Example. Repair of Extrusion of Non-manifold Sections

3.11.1 Extrusion of Non-Manifold Cross Section

3.11.2 Manifold Repair

3.12 E