#1
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Topology
Topology is the study of shapes and spaces.
What happens if one allows geometric objects to be stretched or squeezed but not broken? In fact theres quite a bit of structure in what remains, which is the principal subject of study in topology. |
#2
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Topology studies properties of spaces that are invariant under any continuous deformation. It is sometimes called "rubber-sheet geometry" because the objects can be stretched and contracted like rubber, but cannot be broken. For example, a square can be deformed into a circle without breaking it, but a figure 8 cannot. Hence a square is topologically equivalent to a circle, but different from a figure 8. https://uwaterloo.ca/pure-mathematic...at-is-topology |
#3
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Topology is used in many branches of mathematics, such as differentiable equations, dynamical systems, knot theory, and Riemann surfaces in complex analysis. It is also used in string theory in physics, and for describing the space-time structure of universe. |
#4
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Topology is the mathematical study of the properties that are preserved through deformations, twistings, and stretchings of objects. Tearing, however, is not allowed. A circle is topologically equivalent to an ellipse (into which it can be deformed by stretching) and a sphere is equivalent to an ellipsoid. Similarly, the set of all possible positions of the hour hand of a clock is topologically equivalent to a circle (i.e., a one-dimensional closed curve with no intersections that can be embedded in two-dimensional space), the set of all possible positions of the hour and minute hands taken together is topologically equivalent to the surface of a torus (i.e., a two-dimensional a surface that can be embedded in three-dimensional space), and the set of all possible positions of the hour, minute, and second hands taken together are topologically equivalent to a three-dimensional object. https://mathworld.wolfram.com/Topology.html |
หัวข้อคล้ายคลึงกัน | ||||
หัวข้อ | ผู้ตั้งหัวข้อ | ห้อง | คำตอบ | ข้อความล่าสุด |
ช่วยแก้โจทย์ Topology ให้ทีครับ | Pattern&Math | คณิตศาสตร์อุดมศึกษา | 22 | 12 มกราคม 2013 08:18 |
ช่วยแนะนำหนังสือเกี่ยวกับหัวข้อวิชา Topology ให้หน่อยครับ | Pattern&Math | ฟรีสไตล์ | 0 | 10 มกราคม 2013 17:48 |
ถามปัญหา topology เบื้องต้นหน่อยครับ | phoneee | คณิตศาสตร์อุดมศึกษา | 2 | 19 กุมภาพันธ์ 2010 13:52 |
Topology 2 ข้อ ช่วยทำหน่อยคะ | meezcooter | คณิตศาสตร์อุดมศึกษา | 1 | 03 ธันวาคม 2008 09:46 |
topology เกี่ยวกับเซตปิด | chaitung | คณิตศาสตร์อุดมศึกษา | 3 | 10 พฤศจิกายน 2006 00:27 |
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