f is said to be an open mapping iff the image by f of any open set is open. Let TI be the lower limit topology generated by all unions of intervals of the form {[a,b):a,beR,asb} and let T be the Euclidean topology on R. Let f be the identity map from (R.T) to (R,TI), then: * f is continuous but not open f is open but not continuous f is a homeomorphism f is neither open nor continuous

f is said to be an open mapping iff the image by f of any open set is open. Let TI be the lower limit topology generated by all unions of intervals of the form {[a,b):a,beR,asb} and let T be the Euclidean topology on R. Let f be the identity map from (R.T) to (R,TI), then: * f is continuous but not open f is open but not continuous f is a homeomorphism f is neither open nor continuous

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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f is said to be an open mapping iff the image by f of any open set is open. Let TI be the lower limit topology generated by all unions of intervals of the form {[a,b):a,beR,asb} and let T be the Euclidean topology on R. Let f be the identity map from (R.T) to (R,TI), then: O fis continuous but not open O fis a homeomorphism O fis neither open nor continuous O fis open but not continuous
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f is said to be an open mapping iff the image by f of any open set is open. Let TI be the lower limit topology generated by all unions of intervals of the form {[a,b):a,beR,asb) and let T be the Euclidean topology on R. Let f be the identity map from (R.T) to (R,TI), then: * O fis open but not continuous f is neither open nor continuous f is continuous but not open O fis a homeomorphism Let d(x.y) IVx-1/yl be a metric on R(O}XR(O}. Then the open ball of center 12 and radius /3 is None of the choices 1/6, 2/5
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