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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

Why is it important to understand the presence of bias?

Understanding the presence of bias is important because it allows us to critically evaluate information and make informed decisions. Bias can influence the way we perceive and interpret information, leading to unfair judgments or decisions. By being aware of bias, we can strive for more objective and just outcomes in various aspects of our lives.

What are the advantages and disadvantages of internal bus?

The advantages of an internal bus include simplicity and cost-effectiveness, as it allows for direct communication between components within a computer without the need for additional hardware. It can also enhance performance by facilitating faster data transfer between the CPU, memory, and other components. However, the disadvantages include potential bottlenecks, as multiple devices sharing the same bus can lead to congestion and slower performance. Additionally, the limited bandwidth of the internal bus can restrict the overall system performance, especially in data-intensive applications.

What is the circumfrance of a circle that is 50ft in diameter?

The formula for the circumference of a circle is π x d (diameter).

Solution: C= π x d; C=3.1416 x 50; C=157.08 feet or 157 feet (rounded to nearest whole number).

What makes polyester make it better than other plastics?

Polyester is favored for its durability, strong fibers, and resistance to shrinking and stretching. It is also less prone to wrinkling compared to other plastics, making it a popular choice for clothing and textiles. Additionally, polyester is moisture-wicking and dries quickly.

What companies using the bus topology?

Bus topology is less common in modern networking due to its limitations, but it is still used by some small businesses and educational institutions for simple local area networks (LANs). Companies that require straightforward setups and have limited budgets may utilize bus topology for connecting devices like computers and printers in a single line. However, it's important to note that larger organizations typically opt for more robust topologies, such as star or mesh, to enhance reliability and performance.

What is the common network of bus topology?

The common network of bus topology is a network where clients are connected through cables called a bus. You can learn more about this at the Wikipedia. Once on the website, type "Bus network" into the search field at the top of the page and press enter to bring up the information.

Does a physical network topology specify connectivity methods?

No, physical connections are OSI layer 2 connections and shouldn't specify any higher-level connectivity. Ideally you should still try to draw them in hierarchical order (core, distribution & access).

What is parallelepiped?

A prism whose bases are parallelogram

Where can one find information on tree topology?

You can find information on tree topology in networking textbooks, online resources such as websites, forums, and tutorials, and through professional courses or certifications in networking. Additionally, attending networking conferences or webinars can also provide insights into tree topology and its applications in networking.

What are the characteristics of a star network?

A star network has the clear visual characteristic of the different points on the network being in the shape of a star. This means that there is one central node and all the other nodes connect to it .

What is the equivalent fractions of?

1/2 = 2/4 = 4/8 are three different looking fractions that all mean the same, and are equivalent fractions.

What is the difference between direct proportions and inverse proportions?

The easiest way to think about this is by example:

Direct Proportionality:

"A isproportionalto B"

That means A is equal to the product of B and some constant (usually denoted as k).

A = kB, where k is some constant


Simply put, if A goes up in value, than B goes up in value. If A goes down in value, B also goes down in value. They key here is A and B are either both in the numerator (top of a fraction) or the denominator (bottom).


(1/A) = k(1/B), where k is some constant

This time both A and B are in the denominator, but that's okay because they are BOTH in the denominator.



Inverse Proportionality:

"A is inversely proportional to B"

If A is in the numerator, B is in the denominator, and vice versa.

A = k(1/B)

(1/A) = kB

Simply put, if A goes up B goes down. If A goes down, B goes up.

What is topological space?

The wikipedia article says, 'The definition of a topological space relies only upon

set theory and is the most general notion of a mathematical "space" that allows for the definition of concepts such as continuity, connectedness, and convergence.'


These are abstract spaces where distance is, in some sense, ignored. When Euler considered the 'seven bridges of Koenigsberg problem', for instance, he appreciated that he was ignoring the distances between the bridges and was considering only how they were connected--so that someone could traverse each of them just once. Since that time, of course, the idea of a topological space has permeated many areas of mathematics.


See the related link.

Where do bus topology usually used?

Bus topology is commonly used in small networks or for temporary setups, such as in local area networks (LANs) where the cost of cabling needs to be minimized. It is often utilized in environments like office buildings, schools, and during events where quick and easy installation is required. However, due to its limitations in scalability and fault tolerance, it is less common in larger or more critical network infrastructures.

What is advantage of ring topology?

a ring can operate as a communicationnetwork if it perform the following three functions. 1.data insertion 2.data reception 3.data removal

1.these functions are mainly provided by the repeaters.

2.each repeater also act as the device attachment point. hence the function of data insertion is accomplished by the repeaters.

3.data is transmitted in the form of packets.

4.each packets consists of a destination addrtess field.as this packet by a repeater , the destination address field is