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April 23, 2010 / porton

My research plan

I ‘ve said that I take a vacation in my math research work in order to write a religious book. Unexpectedly quickly I have already finished to write and publish this book and return to my mathematical research.

Now having researched enough about funcoids and reloids (despite of there are yet several open problems in that field), I decided from the next Morning to switch to research of n-ary funcoids and n-ary reloids (where n may be a natural number but may be an arbitrary ordinal or even an arbitrary set). What I previously researched then can be called binary (2-ary) funcoids and binary (2-ary) reloids.

Why I turned to multidimensional funcoid? The reason is that these are necessary for research of generalized limit of n-ary functions. My generalized limit is a generalization of limit for the case of arbitrary (discontinuous) functions. The study of limits is the most practical (regarding the near future) aspect of my Algebraic General Topology research. It seems that generalized limits can be applied to solve practical problems right away. I think, that will also influence the theory of differential equations (which I almost completely forgotten from the time I studied in an university).


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