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2.4.1 Remarks

  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 –
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Belgium seeks cultural prize for famous fries
Communities across Belgium are uniting in a fight for their country's fries to attain cultural heritage status. Jennifer Davis reports. Subscribe: http://smarturl.it/reuterssubscribe More updates and breaking news: http://smarturl.it/BreakingNews Reuters tells the world's stories like no one else. As the largest international multimedia news provider, Reuters provides coverage around the globe and across topics including business, financial, national, and international news. For over 160 years
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3.4 The mass production of death

Mass shootings by soldiers and Einsatzgruppen and the use of the mobile gas vans took time and energy. There was concern about the effects on the morale of the men involved. Towards the end of 1941, even before the Wannsee Conference, the Nazis had begun building camps in Poland that incorporated large gas chambers for the mass production of death. Belzec was the first to come into operation in February 1942, killing people with carbon monoxide first released from bottles and subsequen
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5.2 Technique 2: Relaxation

Here are three relaxation techniques, which you can use before and during the exam.


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5 Unit summary

At the beginning of the period you've studied in this unit, English was an important written language, but was still secondary in status to Latin in the domains of Church and scholarship. Political and social changes combine to have an impact on English; the events of this period demonstrate too the impact of extremely significant technologies. Interest in the English language grew, as evidenced by the beginning of practices that are still key in language description and analysis such as the
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2.2 We are part of nature

Take a few minutes to look around at your surroundings before you read on. What do you see? Obviously this depends on where you are at the moment: at home, at work, or perhaps travelling in between, or maybe you have the misfortune to be laid up in hospital. Possibly like me you are at home. I am fortunate to have a study where I do much of my writing and you won't be surprised to hear that I'm looking at a computer screen at the moment. What else can I see? Books and bookshelves, furniture o
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World of Biology
The World of Biology features engaging stories on all things biology, from bird or insect ecology, to nervous system physiology, to predictions of species' ranges. Each story has a main page and subpages (found in the right-hand menu). Most of our stories also have an associated quiz set. Created by Arizona State University's Ask A Biologist.
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Modern Samba Dance Steps : How to Warm Up to Dance the Samba
Want to Samba? Learn the right way to warm up for dancing the samba in this free dance lesson from professional samba dancers. (1:47)
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1.5 Signal transduction mechanisms

Signalling information has to be transmitted from the receptor in the plasma membrane across the cytoplasm to the nucleus (if gene transcription is the response), the cytoskeleton (if cell movement, or another change to cell morphology, is the response), or various other subcellular compartments. The transmission of a signal must occur in a time-frame appropriate for the cellular response. So, signal transduction needs to take place over both space and time. We have already described a simple
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ワークスペースの確認
このビデオでは、InDesign CS5のワークスペースを確認していきます。
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Facilitating creative thinking
How do you solve your problems? This album follows two facilitators as they lead a 2-day workshop in creative problem-solving, providing a chance to adopt a new approach to the difficulties we encounter in our daily lives. Their reflections on time-keeping and good facilitation provide insight whilst the group tackle problems they’ve experienced at work, using different processes and techniques. This material forms part of The Open University course B822, Creativity, innovation and change.
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Except for third party materials and otherwise stated (see http://www.open.ac.uk/conditions terms and conditions), this content is made available under a http://creativecommons.org/licenses/by-nc-sa/2

Arsenic and Lace – Secret Methods of Old Master Painters
UCL Lunch Hour Lectures are open and free to the public and take place on Tuesdays and Thursdays in the Darwin Lecture Theatre, UCL, Gower Street, London WC1E 6BT. They will resume in Autumn 2008. In the meantime, a number are available below.
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France goes to polls with National Front in ascendancy
Voting begins in the first round of French local elections, as the anti-immigration National Front hopes to consolidate leader Marine Le Pen's bid for the presidency in 2017. Pavithra George reports. Subscribe: http://smarturl.it/reuterssubscribe More updates and breaking news: http://smarturl.it/BreakingNews Reuters tells the world's stories like no one else. As the largest international multimedia news provider, Reuters provides coverage around the globe and across topics including business,
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Nudging people to make better choices: transport applications
Dr Erel Avineri (Reader in Travel Behaviour, UWE, Bristol) talks on 'Nudging people to make better choices: transport applications' as part of the OxTran Seminar Series at the Transport Studies Unit, University of Oxford in 2008.
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Termodinámica Aplicada
La asignatura de Termodinámica Aplicada pertenece a la materia de Ingeniería Energética. Después de cursar esta asignatura los alumnos deberán alcanzar un conocimiento de los conceptos elementales de la Termodinámica. Deberán ser capaces de aplicar los conocimientos básicos de la profesión relacionados con el análisis de sistemas térmicos y energéticos, es la base a utilizar para el desarrollo de otras competencias dentro del campo de la ingeniería térmica en la industria. Se fomen
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Radiation Treatment and Metastatic Spine Disease
Metastatic disease to the spine can be very common in cancer patients. While this condition can often be present without any symptoms, it can often present with pain and neurological symptoms. In this program, Dr. Jason Rockhill explains one effective non-operative treatment for cancer to the spine: radiation. Dr. Michael Lee then discusses metastatic spine disease and Dr. Fangyi Zhang closes the program with some relevant case studies.
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3.5 A new life

There is a common belief that life begins at the moment of conception, i.e. when a sperm fuses with an egg. This is a step forward from past years, when life was alleged to start at the time of ‘quickening’, i.e. when a woman could feel her fetus moving inside her. However, both these opinions suffer from an underlying falsehood: that life ‘begins’ at all. Life is a continuum; gametes are produced by living parents, and fuse to produce new living individuals, but unfused gametes are n
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Acknowledgements

Unit image

Adapted from the works of Steve Jurvetson: [Details correct as of 8th July 2008]

All other material contained within this unit originated at The Open University.

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1. Join over 200,000 students, currently studying with The Open University Author(s): The Open University

2.1.1 Ron revisited

In Case Report 1 you met Ron. Ron is 59 years old, has a BMI of 31 and a central obesity ratio of 0.96, indicating that he is moderately obese, with the fat concentrated in his abdomen, rather than his hips. Clearly a number of factors, some environmental, others relating to Ron's age and all interacting with Ron's genetic constitution, may help to provide an explanation. Let's look at some of these factors in a little more detail. It is clear that Ron enjoys a comfortable lifestyle with litt
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