ABSTRACT
Topology i s a s tudy of internal s tructures of objects a nd mutual position of t he points within objects. While in geometry it is important how far a point is from another point, or if the object is straight or curved, in topology that is almost irrelevant. For example, from a topological point of view, a st raight line is the same as a bent line: the mutual, internal relationships of the points in both objects are essentially the same. Similarly, in topology, a sphere and a crumpled sphere can be considered as being of the same internal structure. In this chapter, we will provide intuitive de nitions of some main topological notions, and then we will brie y and informally consider various topological spaces and some of their properties. Ā e reader should be aware that all the notions we encounter in this chapter have formal and precise counterparts within topology and algebraic topology, the two important mathematical areas.
