0
I know if the set A , the closure of A is connected sure A also connected but the converse Iam not sure
Wiki User
∙ 15y ago
Add your answer:
Earn +20 pts
Prove that comb space in a topological space is an example for connectednes but not locally connectedness?
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.
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.
What postulates states that a quantity must be equal to itself symmetric identity reflexive closure?
Which of the following postulates states that a quantity must be equal to itself
How are the spheres connected?
They are connected by.......~ Having the word sphere in it.....~ All of them play a big role in our worlds environment~
How many faces edges and vertices do connected pyramid have?
A Connected Pyramids have 10 Faces, 12 Vertices, 20 Edges.
Are closure and interiors of connected sets always connected?
Are the closures and interiors of connected sets always connected, or the set of interior points? The Answer: No. There isn't always a connection inside connected sets.
Where would you place the stethoscope for the closure of the tricuspid valve?
In the forth intercostal space, right to the sternum, probably.
What is Cl short for in topology?
Cl is often used as shorthand for closure, e.g. if B, tis a topological space then Cl B is the closure of B. The closure of a topological space B, t is defined as the intersection of all of the closed sets containing B. The closure of C ⊂ B where B, D is a metric space is defined as all of the elements of B that have a 0 metric with C, written asCl C = {b Є B | D(b, C) = 0}.See related links.
What does it mean to dream of a past lover who has died and you need closure?
Dreams are just dreams. If you need closure then you need to grieve properly, give yourself the space and time to do this. Walking in the countryside will help.
What has the author Arnold A Gaerny written?
Arnold A. Gaerny has written: 'Removable closure of the interdental space (C.I.S.)' -- subject(s): Prosthodontics, Dentistry 'Removable closure of the interdental space (C.I.S.) With special consideration of the construction technique for individually milled attachments' -- subject(s): Partial dentures
What is the principles of continuity and closure that best illustrates?
The principle of continuity states that when things are connected, people tend to see them as one object, not their various parts. The principle of closure states that the person's mind tends to see complete figures even if they are incomplete.
How a kaleen closure is different from positive closure?
The main difference between Kaleen closure and positive closure is; the positive closure does not contains the null, but Kaleen closure can contain the null.
What has the author Albert Jarvis written?
Albert Jarvis has written: 'The role of dental caries in space closure in the mixed dentition'
How are sports bras connected to space exploration?
Slag?
What is the closure of the set?
it is the closure of the set
What are the release dates for SoCal Connected - 2008 Private Space Flight?
SoCal Connected - 2008 Private Space Flight was released on: USA: 12 November 2011
Is the closure on the Adult Adam and Eve costume a zipper closure or velcro?
There is a zipper closure.
