3. Let X + 0 be a topological space. a) Show that if {U: | i € I} is a (finite or infinite) open cover of X, then dim X = supier dim Uj. b) Compute the dimension of Va(Tf – T, T?T, – T?T2) CA³. c) Compute the dimension of V,(TỶ – T3,T?T, – T}T2) C P³.

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ISBN:9780470458365
Author:Erwin Kreyszig
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3.
Let X + 0 be a topological space.
a) Show that if {U; | i € I} is a (finite or infinite) open cover of X, then
dim X = supiEJ dim Ui.
b) Compute the dimension of Va(T? – Tỷ, T?T, – TT;) C A³.
c) Compute the dimension of V,(Tỉ – T,TT1 – TT2) C P³.
Transcribed Image Text:3. Let X + 0 be a topological space. a) Show that if {U; | i € I} is a (finite or infinite) open cover of X, then dim X = supiEJ dim Ui. b) Compute the dimension of Va(T? – Tỷ, T?T, – TT;) C A³. c) Compute the dimension of V,(Tỉ – T,TT1 – TT2) C P³.
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