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2. Consider the topology 7, = {X,ø,{a},{b,c}}_on X = {a,b,c} and 1, = {Y,ø.{u}} Y = {u,v} . the topology Note that on {(a,u),(a,v),(b,u),(b,v),(c,u),(c,v)} is the product set on which the product topology is defined. Determine the following: XxY = a) II.'(x) b) II,'(0) c) II.'(a) d) II,'(b,c) e) II, (u)

2. Consider the topology 7, = {X,ø,{a},{b,c}}_on X = {a,b,c} and 1, = {Y,ø.{u}} Y = {u,v} . the topology Note that on {(a,u),(a,v),(b,u),(b,v),(c,u),(c,v)} is the product set on which the product topology is defined. Determine the following: XxY = a) II.'(x) b) II,'(0) c) II.'(a) d) II,'(b,c) e) II, (u)

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.2: Inner Product Spaces
Problem 94E
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2. Consider the topology 7, = {X,ø,{a},{b,c}}_on X = {a,b,c} and T; = {Y,. {u}} Y = {u,v} . the topology Note that on {(a,u),(a,v),(b,u),(b,v),(c,u),(c,v)} is the product set on which the product topology is defined. Determine the following: XxY = a) II.'(x) b) II,'(0) c) II.'(a) d) II,'(b,c) e) II, (u)
Transcribed Image Text:2. Consider the topology 7, = {X,ø,{a},{b,c}}_on X = {a,b,c} and T; = {Y,. {u}} Y = {u,v} . the topology Note that on {(a,u),(a,v),(b,u),(b,v),(c,u),(c,v)} is the product set on which the product topology is defined. Determine the following: XxY = a) II.'(x) b) II,'(0) c) II.'(a) d) II,'(b,c) e) II, (u)
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