While reflecting on my last research paper (currently in the hands of a referee) I discovered a closely related pair of problems that, as far as I can tell from published record, nobody else has considered.
For those interested in topology, the problems concern a property of first-category continuous images of the half-open interval of reals. The property has previously only been of interest in compact spaces, but I want investigate for other classes of spaces.
A solution to one or both would make for a nice paper I think. I've been thinking about them for a couple of weeks with basically no progress.
Should I just tack the problems at the end of my research paper (give up?), or keep them to myself and hope to eventually solve one?