In this paper, we review two properties of completeness known as the Bourbaki-completeness and cofinal in setting metric spaces. These notions came from new classes generalized Cauchy sequences appearing when characterizing so-called Bourbaki-boundedness a similar way that characterize totally boundedness. For clustering Bourbaki–Cauchy cofinally sequences, have respectively what is call The to...

We show that computation of the SPERNER problem is PPA-complete on Möbius band under proper boundary conditions, settling a long term open problem. Further, same computational complexity results extend to other discrete fixed points band, such as Brouwer point problem, DPZP and simple version Tucker well projective plane Klein bottle. expect it opens up new route for further studies related com...

For G a group definable in some structure M , we define notions of “definable” compactification of G and “definable” action of G on a compact space X (definable G-flow), where the latter is under a definability of types assumption on M . We describe the universal definable compactification of G as G∗/(G∗)00 M and the universal definable G-ambit as the type space SG(M). We also point out the exi...