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Next: 2.11.3 Domain Descriptions Up: 2.11 Interval Function Domains Previous: 2.11.1 Interval Inclusion

2.11.2 Interval Extension

The interval extension tex2html_wrap_inline33235 of the m-ary g is also defined in two parts:

math8426

The first part,

math8437

defines the value of tex2html_wrap_inline33249 . The demotions tex2html_wrap_inline33251 and tex2html_wrap_inline33253 gracefully handle undefined domains. When tex2html_wrap_inline33221 is undefined, tex2html_wrap_inline33257 and tex2html_wrap_inline33259 may take on any value. The second part,

figure8448

defines the domain of tex2html_wrap_inline33249 .

The demotions tex2html_wrap_inline33263 and tex2html_wrap_inline33265 demote arbitrary functions, which map parameters to booleans (defined/undefined), to functions which are of the form permitted by tex2html_wrap_inline33267 . The mapping from parameters to booleans is done in two stages: first, the parameters are mapped to extended reals and then those extended reals are mapped to booleans, via tex2html_wrap_inline33269 . The downward demotion tex2html_wrap_inline33263 must preserve domain classifications:

math8459

any valid tex2html_wrap_inline33273 demotion operator is a valid tex2html_wrap_inline33263 demotion operator. The upward demotion tex2html_wrap_inline33265 must also preserve domain classifications:

math8469

any valid tex2html_wrap_inline33279 demotion operator is a valid tex2html_wrap_inline33265 demotion operator.


next up previous notation contents
Next: 2.11.3 Domain Descriptions Up: 2.11 Interval Function Domains Previous: 2.11.1 Interval Inclusion
Jeff TupperMarch 1996