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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
An isometry is a transformation in which the original figure and its image are congruent.
Shape remains constant as size increases.
Azimuth is a technical mapping term which is used to describe the direction of angle between north and south on a compass circle through which the circle line passes.
3 What is the value or Pie to the 100th decimal place?
solution for nth decimal place in pi value
----------------------------------------------------------------
int i=1,rem = 22%7,result=22/7;
while(i<=n)
{
rem = rem*10;
result = rem/7;
rem = rem%7;
i++;
}
printf("nth decimal%d",result);
input: 15(means 15th decimal place in pi value)...
What is the purpose of a circumcenter Why do you use it?
Once the circumcenter is found, each segment connecting each point of the triangle to the cirumcenter are equivalent, so you can put something equidistant to 3 places. Like a hospital equidistant to 3 cities.
What is homotopy in mathematics?
This article is about topology. For chemistry, see Homotopic groups.
The two bold paths shown above are homotopic relative to their endpoints. Thin lines mark isocontours of one possible homotopy.
In topology, two continuous functions from one topological space to another are called homotopic (Greek homos = identical and topos = place) if one can be "continuously deformed" into the other, such a deformation being called a homotopy between the two functions. An outstanding use of homotopy is the definition of homotopy groups and cohomotopy groups, important invariants in algebraic topology. In practice, there are technical difficulties in using homotopies with certain pathological spaces. Consequently most algebraic topologists work with compactly generated spaces, CW complexes, or spectra.
Closure of a connected space is connected?
I know if the set A , the closure of A is connected sure A also connected but the converse Iam not sure
What is the difference between a ratio and a proportion?
a ratio is a comparison between 2 things and a proportion is a ratio on each side of the = sign
You can use a method called the box method.
turn graph paper diagonally and draw lines that way as well if that helps you
What is the continuity in mathematics?
Continuity in mathematics is the first derivative equal to zero or the Boundary condition.
Advantages and disadvantages of network topology?
GO TO armsitgs.wetpaint.com and they have a lot of stuff over topologies it could really help you
Rotations, reflections, and translations are all isometries while a dilation isn't because it doesn't preserve distance
Where are some pictures of real life congruent figures?
our eyes , petals of flowers,wheels of car , bathroom tiles,butterfly's wings,our ears ,cigarettes . :)
How do you calculate the area of a rectangle land whose lengths and widths are different?
Area= width x length
Alternatively, area of irregular or regular polygons can be calculated using SketchAndCalc (see related links below). A free Area and Perimeter Calculator that calculates the area of any shape you draw, regardless of scale or complexity.
What are the subset of a line?
The line, itself, is a subset (though not a proper subset).
A ray is a subset of a line with one end-point which extends in only one direction.
A line segment is a subset of a line with two end points.
A point is a subset of a line.
Finally, nothing is a subset (the null subset) of a line.
In the branch of mathematics called differential geometry, an affine connection is a geometrical object on a smooth manifold which connects nearby tangent spaces, and so permits tangent vector fields to be differentiated as if they were functions on the manifold with values in a fixed vector space.
What is continuity in mathematics?
This normally refers to continuity as a property of certain functions (mappings). They are called continuous if the output depends in a certain way on the input in that a small alteration in the input only leads to a small alteration in the output. Continuous functions can intuitively be drawn with a pencil without ever stopping and beginning again.
More formally, a map between two topological spaces is continuous if the preimage of every open set in the codomain is an open set in the domain.
It's a weight equal to a load, used to balance that load.
Are the real numbers a borel set?
Yes, since the set of real numbers can be expressed as a countable union of closed sets.
In fact if we're talking about subsets of the real numbers (R), then by definition R is in all sigma-algebras of R including the Borel sigma-algebra, and so is a Borel set.
The comb space C=([0,1]X0) union (KX([0,1]) union (0X{0X1]} where K is the set
1/n where n is an integer. It is made up of vertical lines that make it look like a comb. Each of these vertical lines is joined at the bottom to the y axis. You can see immediately the C is connected since each vertical segment is connected and each vertical segment meets the horizontal segment which is also clearly connected. Now, we need to show it is NOT locally connected.
Note the following are equivalent:
(TFAE)
1. A space X is locally connected 2. Components of open subsets in X are open ( in X) 3. X has a basis consisting of connected subsets
Let V be an open ball with the usual metric in the comb space, which I will call C.
Let's put V at the point (0,1/2) and the ball has radius 1/4. The vertical segments of the comb will be the components of V. All of these are open except for ones along the y axis. So we have the {0,y| which is an element of R2 1/4<y<3/4} is not open. This violates condition 2 and we have C is not locally connected.
Note the comb space is path connected as is the deleted comb space. But the comb space is not path connected.
Disadvantages and advantage of hierarchical topology?
is rapid
fast
but it
dont have paths if a line brokes
