Let (+) and (Y ,A) be two topological spaces. Let # be a base for A. Prove that a function f :(4’.r)——({Y ,A) is continuous if and only if the inverse image under ¢ of every member of / is a r- open Set 2. Let (X,r) and (Y A) be two topological spaces. Let B be a basefor A. Prove that a function f :(X.r)→(Y,A) is continuous ifand only if the inverse image under of every member of B is ar- open set.

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

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Let (+) and (Y ,A) be two topological spaces. Let # be a base for A. Prove that a function f :(4’.r)——({Y ,A) is continuous if and only if the inverse image under ¢ of every member of / is a r- open Set

2. Let (X,r) and (Y A) be two topological spaces. Let B be a base
for A. Prove that a function f :(X.r)→(Y,A) is continuous if
and only if the inverse image under of every member of B is a
r- open set.

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