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 open but not continuous O fis neither open nor continuous f is continuous but not open O fis a homeomorphism

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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
Transcribed Image Text: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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