Tags » Munkres

Topology Notes: Closed Sets and Limit Points

Definition 1. A subset in a topological space is closed if its complement is open, that is . //

Theorem 2. Let be a topological space, then the following are true: 1,240 more words

Munkres

Topology Notes: Order Topology, Product Topology Of Two Sets and the Subspace Topology

When is a simply ordered set, then there is a topology on that can be easily defined using the order relation and it is called the order topology. 1,662 more words

Munkres

Topology Notes: Topological Spaces and Basis

Definition 1. A topology on a set is a collection of subsets of having the following properties:

1) and are in ;

2) The union of the elements of any subcollection of is in ; 1,309 more words

Munkres

Topology Notes: Relations

These notes have been taken from Munkres, Topology. Sec 3

Relations

Relations can be seen as being generalisations of functions, that is, it is a way of linking together two objects in the same set and not being confined by the restriction that each member of maps to a unique element. 1,292 more words

Munkres

Update 1/15/15

My apologies for the long silence. Finals for high school are in approximately six days from today and I have put in extensive hours into preparing. 219 more words