Proposition 2.3. Let X,Y be (topological) sets containing E and F, re- spectively. Moreover, let & and F be elementary families of X and Y, respectively. Then 8 x F := {E x F |E € 8, FEF} is an elementary family of X × Y. Here, X × Y is defined by X xY := {(x, y) | z € X, y E Y}.

Proposition 2.3. Let X,Y be (topological) sets containing E and F, re- spectively. Moreover, let & and F be elementary families of X and Y, respectively. Then 8 x F := {E x F |E € 8, FEF} is an elementary family of X × Y. Here, X × Y is defined by X xY := {(x, y) | z € X, y E Y}.

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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Concept explainers

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.

Question

Proposition 2.3. Let X, Y be (topological) sets containing E and F, re-
spectively. Moreover, let & and F be elementary families of X and Y,
respectively. Then
Ex F:= {Ex F | E E 8, FEF}
is an elementary family of X x Y. Here, X x Y is defined by
X xY := {(x, y) |z € X, y E Y}.

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