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Topology
While geometry is primarily concerned with the mathematical properties of spatial objects, topology is concerned with the mathematical properties of those objects under continuous deformations. Please post all questions about topological subjects like homeomorphisms, manifolds, convergence, and connectedness, as well as their broad applications in computing, physics, and graph theory, into this category.
1,087 Questions
Prove that Hilbert Space is a Metric Space?
The question doesn't make sense, or alternatively it is true by definition.
A Hilbert Space is a complete inner product space - complete in the metric induced by the norm defined by the inner product over the space.
In other words an inner product space is a vector space with an inner product defined on it.
An inner product then defines a norm on the space, and every norm on a space induces a metric.
A Hilbert Space is thus also a complete metric space, simply where the metric is induced by the inner product.
Isometric stretches are when your muscles are contracted and held that way. It is the opposite of dynamic stretching where your muscles are lengthening and contracting. An example of an isometric stretch is the plank; where you're resting on your forearms and your toes. Your abdominal muscles are being contracted but there is no lengthening and contracting movement. Dynamic stretching would be doing a pushup.
What is the function of the terminator in a bus topology?
To prevent signals from being echoed back through the network
False
There is the Morris number sequence and the Fibonacci number sequence. The Padovan sequence. The Juggler sequence.
I just know the Fibonacci sequence:
0,1,1,2,3,5,8,13,21,34,55,89,144,233,377
Morris number sequence: 1 11 21 1211 111221 312211...
What is an isometry that maps all points of a figure the same distance in the same direction?
translation
What are the parts of a right triangle?
a right triangle has three sides like every triangle. A hypotenuse, which is the side opposite of the right angle, and the other two sides are known as legs. <-- that explains the sides pretty well. The angles are the right angle, of course, which is a perfect 90 degrees and two acute angles which is always going to be less than 90..i don't think there can be any other angles besides the acutes and right angle.
Explain why a glide reflection is an isometry?
Because the glide reflection is a combination of two isometries, it is also an isometry.
Find the number of connections needed to be used in Mesh topology in network of 8 nodes and also find that how many IO ports are needed for each device Also write formulas used to solve this question?
Find the number of connections needed to be used in Mesh topology in network of 8 and also find that how many I/O ports are needed for each device. Also write formulas used to solve this question?
Solution:
Formulas:
To find the no. of links:
= n (n-1)/2
To find the I/O ports:
= n-1
If the network of 8 then
No. of Links = n (n-1)/2
= 8(8-1)/2
=8(7)/2
=56/2
=28 ANS
No. of I/O ports: = n-1
=8-1
=7 ANS
What is isometries rigid transformations?
I think "isometries" and "rigid transformation" are two different names for the same thing. Look for "isometry" on wikipedia.
A Star Network Topology is best suited for smaller networks and works efficiently when there is limited number of nodes. One has to ensure that the hub or the central node is always working and extra security features should be added to the hub because it s the heart of the network
What transformation is not an isometry?
Dilation - the image created is not congruent to the pre-image
How do you rotate a figure 360 degrees clockwise on a graph?
360 degree rotation (clockwise or anticlockwise) leaves any figure in exactly the same position as it was at the start. So YOU DO NOTHING.
