We can insert half-twists into a paper surface whenever a piece of the surface is homeomorphic to a rectangle ABCD with the following properties:

the edges AB and CD of the rectangle map to distinct parts of the boundary of the surface, and the edges BC and DA of the rectangle map to non-boundary points of the surface.

As illustrated in Author(s): The Open University

1. This theorem applies to all surfaces and not just to surfaces in space.

2. This theorem tells us that the boundary number is a topological invariant for surfaces, i.e. a property that is invariant under homeomorphisms.

3. It follows from the theorem that two surfaces with different boundary numbers cannot be homeomorphic. It does not follow that two surfaces with the same boundary number are homeomorphic â€“
Author(s): The Open University

In this section we show how to construct surfaces by taking a piece of paper in the shape of a polygon and gluing some of its edges together. The surfaces that we obtain occupy a central position in this course, as you will see.

Author(s): The Open University

Two topological spaces (X, TX) and (Y, TY) are homeomorphic if there is a bijection f : X â†’ Y that is continuous, and whose inverse fâˆ’1 is also continuous, with respect to the given topologies; such a function f is called a homeomorphism. The relation â€˜is homeomorphic toâ€™ between topological spaces is the most fundamental relation in topology, because two topological spaces that are homeomo
Author(s): The Open University

A genre is a particular type or category of fiction. It can apply to both the long and short form (
Author(s): The Open University

• Use a journal to build ideas for character.
• Consider all the influences that go into the making of your character: age, gender, race, nationality, marital status, religion, profession.
• Know about your character's inner life: what s/he wants, thinks, remembers, resents, fears, dreams, denies.
• Know about your character's behaviour, what s/he wears, buys, eats, says, works at and plays at.
• Know how your character speaks and how this
Author(s): The Open University

How teams work
This free course, How teams work, provides an introduction to working in virtual project teams by explaining terms and concepts related to teams and to projects. The complexity of the interaction of people and technology is highlighted. First published on Tue, 15 Mar 2011 as Author(s): Creator not set

This free course was written by The Open University

Except for third party materials and otherwise stated (see terms and conditions ), this content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 Licence .

The material acknowle
Author(s): The Open University

It is common to shortlist up to six applicants per position, but the exact number may reflect the time you have available for interviewing and the strength of the applicants. The important point is to ensure that as far as possible you finish up with the best possible candidates on the shortlist. This can best be achieved by approaching the task systematically. In other words, the systematic use of criteria as detailed in the job specification should be preferred to reliance on intuition. It
Author(s): The Open University

Themes and theories for working in virtual project teams
This free course, Themes and theories for working in virtual project teams, offers an introduction to working in virtual project teams. It explains the terms and concepts related to teams and projects, and highlights the complexity around the interaction of people and technology. First published on Tue, 15 Mar 2016 as Author(s): Creator not set

The impact of technology on children's physical activity
This free course, The impact of technology on children's physical activity, explores the impact of technology on childrenâ€™s physical activity levels. It examines the different types of technology that children have access to and the ways in which they engage with it. As part of this discussion this course looks at information from a range of different sources and evaluates this evidence to try and answer the question of whether technology is helping or hindering childrenâ€™s physical activity
Author(s): Creator not set

The primary functions of the ATM layer are associated with the routing and switching of ATM cells. Because ATM cells are packets, the switches are packet switches and the switching operation can be called forwarding, but by convention, because the ATM layer provides a connection-oriented service, the term â€˜forwardingâ€™ is generally not used.

The path cells take and the resources allocated to them depend on their service category. This is determined when a virtual connection is
Author(s): The Open University

TCP does not assume a reliable communication network and takes precautions against the loss or duplication of protocol data units. One method is the three-way handshake procedure for establishing a connection between two hosts. Figure 18 shows the TCP procedure for this. This connection is a virtual connection of the type described in Section 2; many virtual connections can share a physical communication channel.

Author(s): The Open University

The Internet is a worldwide public internetwork, which allows computers to communicate with each other even though they may have different manufacturers and different operating systems. The origins of the Internet lie in a project of the US Defense Advanced Research Project Agency in the 1970s, where it was intended to foster communication between research institutions rather than operate for profit. However, a substantial amount of traffic carried by the Internet is now related to com
Author(s): The Open University

You have already seen that operating systems organise the sharing of resources. But they do much more than this; they ensure the efficient running of a computer by:

• loading application programs from secondary memory into main memory and managing their execution;

• supporting application programs by managing their use of the computer's resources;

• managing the storage of programs and data in secondary memory;

• ac
Author(s): The Open University

The last computer I am going to look at is the embedded computer in a digital camera.

Figure 10 shows a picture of a digital camera. The screen of the camera is displaying a picture that has previously been stored in a memory card within the camera. This memory card is not the camera computer's main memory, nor is it the secondary memory used to hold the computer's program; it is a form of removable secondary memory where the computer stores the images taken. Next to the camera in Figur
Author(s): The Open University

A set of electronic kitchen scales is shown in Figure 7. Their basic operation is relatively simple. When they are switched on and, for example, a 500-gram object is placed in the scalepan, the display shows the digits 500 and the letter g.

Over the following screens you will look at three different examples of computers: a PC, which is obviously a computer, and a set of electronic kitchen scales and a digital camera, which are not so obviously computers. You will find that all three of these examples match with the functional block diagram of a computer given in
Author(s): The Open University

But if all the data and computer instructions within a computer are represented by 1s and 0s, how can this limited set of conditions be used to represent, for instance, every letter of the alphabet that might be typed into a computer from a keyboard? Activity 4 showed that there are four possible combinations of 1s and 0s i
Author(s): The Open University

In Sections 3.1 and 3.2 you are going to find out a little more about one of the key components of a computer: the processor, which manipulates data according to a list of instructions called a program.

Here is a mini-quiz which explores some facts about processors.

### Question 1

Author(s): The Open University