If the term edge is to define a topological invariant of objects, explain why rectangles, pentagons, octagons, and circles must have the same number of edges. Because a circle has a boundary which is composed of one continuous component we say that it has one edge.

Q: How many edges are in this shape?

A: We have to find the edge of the figure.

Q: Suppose there are 10 points in a plane such that no three points are collinear. How many distinct…

A: Given; There 10 points in a plane such that no three points are collinear

Q: Describe your step-by-step process in deriving the network in item 2. Use flowchart or pseu-…

A: In this question to draw the flow diagram for epidemic  model described in step2

Q: Decide whether the following statement is true of false. Prove your answer: If two graphs have the…

A:

Q: Each node can have at most n=v number of edges. (True means Doğru; False means Yanlış) Birini seçin:…

A: Result: 1. The maximum number of edges in an undirected graph is n(n-1)/2. 2. The maximum number of…

Q: Draw the network diagram for the above project.

A: Network diagram is drawn by connecting nodes through joining lines.

Q: Consider a bipartite network with N, and N, nodes in the two sets. (a) What is the maximum number of…

A: Since you have asked questions with multiple subparts, as per our company guidelines, we have solved…

Q: 1. Explain the relationship between the number of faces and the number of edges in a triangulation.

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: can two disjoint sets be close? Justify your answer using an example.

A: We know that any closed interval of the form [a,b] is an closed set. We use this fact further.

Q: Show that the real line is a metric space.

A: Answer is mentioned below

Q: What is a set? What is a subset? How can we show that a set is equal to another set, using this…

A: To define: the set, subset. To show: a set is equal to another set. Please post the multiple…

Q: Create a Venn diagram to show the hierarchy of triangles, quadrilaterals, isosceles triangles, and…

A: To be constructed : Venn diagram to show the hierarchy of triangles, quadrilaterals, isosceles…

Q: Use graph to find  set. [1, 3) ∩ (0, 4)

A: Given set is  [1, 3) ∩ (0, 4) The graph of the given set is as shown

Q: Show that the average degree of a vertex in the triangulation is strictly less than 6.

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Q: The boundary of a set is equal to the boundary of the complement) True or false

A: (The boundary of a set is equal to the boundary of the complement) True or false

Q: 2. 1. DUKAS 3.

A: Suppose we are tracing the graphs from left to right. While tracing graph 1, we have to stop the…

Q: If you claim that the graphs are isomorphic, show a bijection and show that your bijection preserves…

A: First graph has a cycle of length 3 which is a-b-j-a

Q: Stafe true andwer, your or Confinuous map en a metico is an open map

A:

Q: If countries in the Southeast region are consisting of archipelagos then other foreign countries…

A: Euler diagram is a general diagram giving meaningful information about things that are related to…

Q: The quotient topology actually defines a topology.

A: The quotient topology  actually defines a topology

Q: Provide an example of a topological space that is connected but not path-connected,why?

A: We use definition of connected and path connected sets. We use contradiction method.

Q: How many edges does G have? Explain why. What is the chromatic number of G? Explain why. What is the…

A: This is a problem of Graph Theory.

Q: 10. Consider a finite model for incidence geometry that satisfies the following additional axiom:…

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Q: The usuall metric space (Rd)isComplete ***

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Q: will be prepared using i= 0.5, the lowest clas 18. The true limits or the class boundaries of the…

A: 18 From the part 17, the lowest class interval is (6.4, 6.9).

Q: True or False: The edge set of every closed trail in a graph can be partitioned into edge sets of…

A:

Q: What is the minimum number of points that can be contained in a space

A: There is no minimum number of points to be contained in a space. But if we want to find a location…

Q: 3 5

A: Isomorphism of graph: Let G and H be two graphs. They are said to be isomorphic if there exists a…

Q: Question 2: Show that path connectedness is a topological property. Explain and show your work.

A: a property of spaces is a topological property if whenever a space X possesses that property every…

Q: Use graph to find set. [3, ∞)∩ (6, ∞)

A: We have to find set using graph for given interval notation: [3, ∞)∩6, ∞ Here there are two set…

Q: How different can two sets of R ^ 2 that have the same boundary be?

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Q: If the Upper-class boundary and class interval are 299 and 100 respectively then what will be the…

A:

Q: Show that if a topological space has a finite number of points each of which is closed then it has…

A: Topology question.

Q: Define the term Connectedness?

A: In mathematics Connectedness is used to refer to various properties meaning, in some sense, "all one…

Q: Show that topologically completeness is weak hereditary property.

A: In this question, we have to show that completeness is a weak hereditary property.

Q: Sketch the region that corresponds to the given inequalities, say whether the region is bounded or…

A: We consider the corresponding equation and draw third graphs. Then we find the area bounded by the…

Q: what ordered pair is an example of a topological space that is connected but not path-connected,why?

A: We use contradiction method.

Q: Define what it means for a topological space to be completely regular,

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Q: topological spaces X and Y,

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Q: The set {0,3} with the usual metric is connected as union of connected sets {0} and {3} True False

A:

Q: what is the minimum size of edge cover ? And give examples

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Q: Recall that a bridge in a connected graph is an edge whose removal disconnects the graph. The…

A: The objective here is to find the maximum number of edges in a graph on 10 vertices that contains a…

Q: If (X, τ) is a topological space and if A,B⊂X Show that ∂(A∩B)⊂∂A∪∂B.

A: Boundary of a set in topological space: Let A be a subset of a topological space X, τ. The boundary…

Q: Write precise mathematical definition for the following terms: a) Eulerian path b) Matching c)…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Construct a graph with vertices P, Q, R, S, T, U whose degrees are 4, 3, 2, 3, 3, 1 What is the edge…

A:

Q: Use graphs to find the set : [3, ∞) ∩ (6, ∞)

A: Given: [3,∞)∩(6,∞)

Q: Given an undirected network of N > 1 nodes which is connected. Which is the maximum diameter?

A: As given by the question There are given that the N>1 connected nodes. According to the maximum…

Q: Is any discrete space complete? Give an example to substantiate your answer.

A: A metric space is complete if and only if every Cauchy sequence is convergent.

Q: Suppose metric space X is not path-wise connected then X is not connected. True False

A: A space is said to be Path connected if we can fine a continuous function between any two points of…