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We can now state the fundamental theorem of model ∞-categories, which says that under the expected co/fibrancy hypotheses, the spaces of left and right homotopy classes of maps

In this paper, first we give a theorem which generalizes the Banach contraction principle and fixed point theorems given by many authors, and then a fixed point theorem for

Finally, in the Appendix, we prove the well-known fact that the category of ket coverings of a connected locally noetherian fs log scheme is a Galois category; this implies,

Then the change of variables, or area formula holds for f provided removing from counting into the multiplicity function the set where f is not approximately H¨ older continuous1.

THEOREM 4.1 Let X be a non-empty convex subset of the locally convex Hausdorff topological vector space E, T an upper hemicontinuous mapping of X into 2 E’, T(x) is a non-empty

[3] Chari, Vyjayanthi, On the fermionic formula and the Kirillov-Reshetikhin conjecture, Int. and Yamada, Y., Remarks on fermionic formula, Contemp. and Tsuboi, Z., Paths, crystals

Next, we will examine the notion of generalization of Ramsey type theorems in the sense of a given zero sum theorem in view of the new

Pro. Solel, Hardy algebras, W ∗ -orrespondenes and inter- polation theory, Math. Popesu, Nonommutative dis algebras and their representations,. Pro. Popesu, Interpolation problems