On thin sets of primes expressible as sumsets
On thin sets of primes expressible as sumsets
We introduce and investigate the notions of weakly pre-<Emphasis Type=ā€¯Italicā€¯>I</Emphasis>-open sets and weakly pre-<Emphasis Type=ā€¯Italicā€¯>I</Emphasis>-continuous functions. By using the results, the following decomposition is provided: a function <Emphasis Type=ā€¯Italicā€¯>f</Emphasis>: (<Emphasis Type=ā€¯Italicā€¯>X</Emphasis>,&tgr;,<Emphasis Type=ā€¯Italicā€¯>I</Emphasis>)→ (<Emphasis Type=ā€¯Italicā€¯>Y</Emphasis>,&sgr;)<InlineEquation><EquationSource=ā€¯texā€¯> is continuous if and only if <Emphasis Type=ā€¯Italicā€¯>f</Emphasis> is weakly pre-<Emphasis Type=ā€¯Italicā€¯>I</Emphasis>-continuous and strongly <Emphasis Type=ā€¯Italicā€¯>B<Subscript>I</Subscript></Emphasis>-continuous.