Elements in the group of symmetries of the given bounded figure.

Question

Q1lal Let X be an arbitrary infinite set and let r the family of all subsets F of X which do not contain a particular point x, EX and the complements F of all finite subsets F of X show that (X.r) is a topology. bl The nbhd system N(x) at x in a topological space X has the following properties NO- N(x) for any xX N1- If N EN(x) then x€N N2- If NEN(x), NCM then MeN(x) N3- If NEN(x), MEN(x) then NOMEN(x) N4- If N = N(x) then 3M = N(x) such that MCN then MeN(y) for any уем Show that there exist a unique topology τ on X. Q2\a\let (X,r) be the topology space and BST show that ẞ is base for a topology on X iff for any G open set xEG then there exist A Eẞ such that x E ACG. b\Let ẞ is a collection of open sets in X show that is base for a topology on X iff for each xex the collection B, (BEB\xEB) is is a nbhd base at x. - Q31 Choose only two: al Let A be a subspace of a space X show that FCA is closed iff F KOA, K is closed set in X. الرياضيات b\ Let X and Y be two topological space and f:X -…

Answer 1

Question

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

Chapter 4.3, Problem 11E

To determine

Elements in the group of symmetries of the given bounded figure.

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Q1lal Let X be an arbitrary infinite set and let r the family of all subsets F of X which do not contain a particular point x, EX and the complements F of all finite subsets F of X show that (X.r) is a topology. bl The nbhd system N(x) at x in a topological space X has the following properties NO- N(x) for any xX N1- If N EN(x) then x€N N2- If NEN(x), NCM then MeN(x) N3- If NEN(x), MEN(x) then NOMEN(x) N4- If N = N(x) then 3M = N(x) such that MCN then MeN(y) for any уем Show that there exist a unique topology τ on X. Q2\a\let (X,r) be the topology space and BST show that ẞ is base for a topology on X iff for any G open set xEG then there exist A Eẞ such that x E ACG. b\Let ẞ is a collection of open sets in X show that is base for a topology on X iff for each xex the collection B, (BEB\xEB) is is a nbhd base at x. - Q31 Choose only two: al Let A be a subspace of a space X show that FCA is closed iff F KOA, K is closed set in X. الرياضيات b\ Let X and Y be two topological space and f:X -…

Q1\ Let X be a topological space and let Int be the interior operation defined on P(X) such that 1₁.Int(X) = X 12. Int (A) CA for each A = P(X) 13. Int (int (A) = Int (A) for each A = P(X) 14. Int (An B) = Int(A) n Int (B) for each A, B = P(X) 15. A is open iff Int (A) = A Show that there exist a unique topology T on X. Q2\ Let X be a topological space and suppose that a nbhd base has been fixed at each x E X and A SCX show that A open iff A contains a basic nbdh of each its point Q3\ Let X be a topological space and and A CX show that A closed set iff every limit point of A is in A. A'S A ACA Q4\ If ẞ is a collection of open sets in X show that ẞ is a base for a topology on X iff for each x E X then ẞx = {BE B|x E B} is a nbhd base at x. Q5\ If A subspace of a topological space X, if x Є A show that V is nbhd of x in A iff V = Un A where U is nbdh of x in X.

+ Theorem: Let be a function from a topological space (X,T) on to a non-empty set y then is a quotient map iff vesy if f(B) is closed in X then & is >Y. ie Bclosed in bp closed in the quotient topology induced by f iff (B) is closed in x- التاريخ Acy الموضوع : Theorem:- IP & and I are topological space and fix sy is continuous او function and either open or closed then the topology Cony is the quatient topology p proof: Theorem: Lety have the quotient topology induced by map f of X onto y. The-x: then an arbirary map g:y 7 is continuous 7. iff gof: x > z is "g of continuous Continuous function f

Answer 2

Question

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

Chapter 4.3, Problem 11E

To determine

Elements in the group of symmetries of the given bounded figure.

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Answer 3

Question

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

Chapter 4.3, Problem 11E

To determine

Elements in the group of symmetries of the given bounded figure.

Expert Solution & Answer

Trending nowThis is a popular solution!

See solution

Check out sample textbook solution

Answer 4

Question

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

Chapter 4.3, Problem 11E

To determine