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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
Is every point of an open set E contained in R2 a limit point of E?
In reply to "limit point", posted by Jennifer on Sept 24, 2004:
>I have a basic question. Thanks a lot.
>
>Is every point of every open set E (is contained in R^2) a limit point of E?
Yes, it is. If O is open and x is in O then some open ball B(x,e) is contained in O
(as x is an interior point of O).
But open balls in R^2 have the property that they contain many more points than just x
(eg also (x_1 + 1/2*e, x_2) for x = (x_1, x_2), and e>0 ) and so if B(x,r) is any neighbourhood
of x, then B(x, min(r,e)) will contain this point, which is in O (as B(x,e) \subset O) and not equal to x.
So x is a limit point of O.
>In case of for clsed sets in R^2?
>
There it fails, eg if C = {(1/n, 0): n in N}.
No point of C is a limit point of C (but (0,0) is), as is easily checked.
Henno
What does it mean for a subspace of a topological space to be ''somewhere dense''?
Somewhere dense is defined to be the following:
Let B, t be a topological space and C ⊂ B. C is somewhere dense if (Cl C)o ≠Ø, the empty set. That is, if the closure of the interior of C has at least one non-empty set.
See related links for more information.
An isometric triangle is a 3 dimensional triangle shown on a flat surface or in 2 dimensions.
What is Free Edges in Hyper mesh?
while meshing the component, some unconnected elements will found, that is known as free edges.
What best describes a network's physical topology?
Physical layout of where the Hosts are located, Location of wires, etc...
It basically means the structure of your network.
Considerations when choosing topology?
The following factors should be considered when choosing a topology:
- Installation
- Maintenance and troubleshooting
- Expected growth
- Distances
- Infrastructure
- Existing network
As a general rule, a bus topology is the cheapest to install, but may be more expensive to maintain because it does not provide for redundancy.
What is the differences between star topology and bus topology?
A star topology has a central hub with other devices each connected to the hub but not to each other - for one device to communicate to another, they have to use the hub.
With a bus topology all the devices are connected to the same bus - there is no hub. Each topology has advantages and disadvantages; the speed of a star network is limited by the hub; a telephone exchange is an example of a star network and there is a built-in limit to the number of devices that can be connected and there's no way to increase it other than to replace the hub with a bigger one. However, the devices (telephones in our example) can be dumb - all the intelligence is in the hub; it manages the calls and importantly, for commercial exchanges, calculates the bills. For bus networks, devices have to be smarter but can do much more as they can grab the whole bus.
They are spheres. They cannot therefore have different geometrical properties. To alter surface to volume ratios you would need to alter the shape. The study of mathematical shapes is called topology.
An isometry that moves or maps every point of the plane the same distance and direction is a translation, which is one of 4 transformations that can be plotted on the Cartesian plane.
How do you solve lokulus topology challenge?
I'm guessing there are multiple solutions (not sure), but here's how to obtain one solution I found:
- Start by solving design #21 ("Pin the tail on the Black Donkey") as seen in the instruction manual.
- Lift out the two triangles in the center of the donkey together, flip them over, rotate to fit, and place them back down.
**NOTE: If the larger of the two triangles is red when you flip it, switch it with the identically-sized triangle making up the donkey's head. It should have blue as the alternate color.
- Topology Challenge Solved!
Why is a dilation not an isometry?
Because the image is not the same size as the preimage. To do a dilation all you do is make the image smaller or larger than it was before.
What can you do to reduce your risk factors?
To reduce your risk factors, which can help you reduce your chances of getting cancer, you should have a healthy diet and stay away from tobacco.
The assumptions of a metric space except for symmetry.
What kind of topologies are good choices for highly available enterprise networks?
Mesh topologies and SONET rings.
What is the physical network topology in which each node is connected to a central point?
It is called a Star topology
