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N Hid 4. Let T consist of 0, R, and all intervals of the form (-0, p) for p E R. Prove that T is a topology on R. Let X be a set and assume peX Where Iis the collection of all subset of X containing P (1) By the definilion of a Topology x, IRE Ţ. along with 'o and x. So J topology on x. is a (2) Let Ui , Uz E T. Let, U,= (-∞, p.) and Uz =(-@,P.), p. , Pa € IR. Let, p= min{ P., P23 also PE IR Now, U, nUz = l-∞, p)E T. (3) Consider any subcollection in T.If sUcBiEl is any subcollection of in T by de finition each Vi contains (-∞, P) where Pi E IR such that iEl. Let, p = maxs P: 3 also PEIR. NOW, Y Vi = (-0, P)E T. e lements %3D %3D LEI what happens if this max doesn't exist? Hence by al, (2), cus p a topology on IR.

N Hid 4. Let T consist of 0, R, and all intervals of the form (-0, p) for p E R. Prove that T is a topology on R. Let X be a set and assume peX Where Iis the collection of all subset of X containing P (1) By the definilion of a Topology x, IRE Ţ. along with 'o and x. So J topology on x. is a (2) Let Ui , Uz E T. Let, U,= (-∞, p.) and Uz =(-@,P.), p. , Pa € IR. Let, p= min{ P., P23 also PE IR Now, U, nUz = l-∞, p)E T. (3) Consider any subcollection in T.If sUcBiEl is any subcollection of in T by de finition each Vi contains (-∞, P) where Pi E IR such that iEl. Let, p = maxs P: 3 also PEIR. NOW, Y Vi = (-0, P)E T. e lements %3D %3D LEI what happens if this max doesn't exist? Hence by al, (2), cus p a topology on IR.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 78E
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'N Hid 4. Let T consist of 0, R, and all intervals of the form (-∞, p) for p e R. Prove that T is a topology on R. Let X be a set and assume peX Where Iis the collection of all subset of x containing P along with 'o and x So J is a on x. (1) By the definilion of a Topology x, IR E Ţ. topology (2) Let Ui , Uz E T. Let, U,= (-∞, p,) and Vz =(-», P.), P.,pz € IR. Let, p- min{ P., P23 also PE IR. Now, U, nUz = (-0∞,p)E T. %3D T.If {U,}iEl is any subcollection of elements (3) Consider any subcollection in in T by de finition each Vi contains (-o, Pu where Pi E IR such that iel. Let, P= maxs P. 3 also PEIR. NOW, U vi = (-∞, P)E T. LEI what happens if this max doesn't exist? Hence by al, l2l, cus mpU a topology on IR.
Transcribed Image Text:'N Hid 4. Let T consist of 0, R, and all intervals of the form (-∞, p) for p e R. Prove that T is a topology on R. Let X be a set and assume peX Where Iis the collection of all subset of x containing P along with 'o and x So J is a on x. (1) By the definilion of a Topology x, IR E Ţ. topology (2) Let Ui , Uz E T. Let, U,= (-∞, p,) and Vz =(-», P.), P.,pz € IR. Let, p- min{ P., P23 also PE IR. Now, U, nUz = (-0∞,p)E T. %3D T.If {U,}iEl is any subcollection of elements (3) Consider any subcollection in in T by de finition each Vi contains (-o, Pu where Pi E IR such that iel. Let, P= maxs P. 3 also PEIR. NOW, U vi = (-∞, P)E T. LEI what happens if this max doesn't exist? Hence by al, l2l, cus mpU a topology on IR.
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