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March 26, 2010 / porton

New conjectures about complete funcoids and reloids

After removing an erroneous theorem I posed two new open problems to take its place:

Conjecture If f is a complete funcoid and R is a set of funcoids then f \circ \bigcup {\nobreak}^{\mathsf{FCD}} R = \bigcup {\nobreak}^{\mathsf{FCD}} \langle f \circ \rangle R.

Conjecture If f is a complete reloid and R is a set of reloids then f \circ \bigcup {\nobreak}^{\mathsf{RLD}} R = \bigcup {\nobreak}^{\mathsf{RLD}} \langle f \circ \rangle R.

These conjectures may be weakened:

Conjecture If f is a discrete funcoid and R is a set of funcoids then f \circ \bigcup {\nobreak}^{\mathsf{FCD}} R = \bigcup {\nobreak}^{\mathsf{FCD}} \langle f \circ \rangle R.

Conjecture If f is a discrete reloid and R is a set of reloids then f \circ \bigcup {\nobreak}^{\mathsf{RLD}} R = \bigcup {\nobreak}^{\mathsf{RLD}} \langle f \circ \rangle R.

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