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Let X be a set and let TCF(X) = {UCX|X\ U is finite or is all of X}. n (a) Let n € N and let {U₁,…, Un} TcF(X). Show that U₂ € TCF(X). (b) Show that the standard topology Istandard (R) on R is finer than Tcf(R). i=1

Let X be a set and let TCF(X) = {UCX|X\ U is finite or is all of X}. n (a) Let n € N and let {U₁,…, Un} TcF(X). Show that U₂ € TCF(X). (b) Show that the standard topology Istandard (R) on R is finer than Tcf(R). i=1

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Letters A & B

Let X be a set and let TCF(X) = {U CX|X\U is finite or is all of X}. n (a) Let n E N and let {U₁,..., Un} ≤ TCF(X). Show that U₂ € TCF(X). (b) Show that the standard topology Istandard (R) on R is finer than TcF(R). i=1
Transcribed Image Text:Let X be a set and let TCF(X) = {U CX|X\U is finite or is all of X}. n (a) Let n E N and let {U₁,..., Un} ≤ TCF(X). Show that U₂ € TCF(X). (b) Show that the standard topology Istandard (R) on R is finer than TcF(R). i=1
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