**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

**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

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

**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

*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

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

**Jacob Harvey Mason**

b. 6 July 1856, Ervin Township, Howard County, Indiana, to Simon Peter and Elizabeth (White) Mason

d. 7 March 1903, southeastern Woods County, Oklahoma Territory (now Major County) 184 more words