In this case, A and f(A) are both D-open and f#58;A#92;rightarrowf(A) is a diffeomorphism where A and f(A) are equipped with their subset diffeology.
Source: wiktionary
Diffeology
Synonyms for "diffeology"
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And, for #92;mathcal#123;G#125;#42;#47;#92;Gamma and #92;mathcal#123;G#125;'#42;#47;#92;Gamma' equipped with the quotient diffeologies, h#42;#95;#92;Gamma is naturally smooth.
Source: wiktionary
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