Some generalizations of Chirka’s extension theorem

Some Generalizations of Fedorchuk Duality Theorem – I

Generalizing Duality Theorem of V. V. Fedorchuk [11], we prove Stone-type duality theorems for the following four categories: all of them have as objects the locally compact Hausdorff spaces, and their morphisms are, respectively, the continuous skeletal maps, the quasi-open perfect maps, the open maps, the open perfect maps. In particular, a Stone-type duality theorem for the category of all c...

Some generalizations of the MacMahon Master Theorem

We consider a number of generalizations of the β-extended MacMahon Master Theorem for a matrix. The generalizations are based on replacing permutations on multisets formed from matrix indices by partial permutations or derangements over matrix or submatrix indices.

Some Generalizations of Jungck's Fixed Point Theorem

Some Generalizations of Petryshyn’s Theorem and Altman’s Theorem

In this paper, some new fixed point theorems for semi-closed 1-setcontractive operators of functional type are obtained, which generalize the famous Petryshyn’s theorem and Altman’s theorem by replacing the norm with some classes of functionals.

Some Applications of Ball’s Extension Theorem

We present two applications Ball’s extension theorem. First we observe that Ball’s extension theorem, together with the recent solution of Ball’s Markov type 2 problem due to Naor, Peres, Schramm and Sheffilield, imply a generalization, and an alternative proof of, the Johnson-Lindenstrauss extension theorem. Secondly, we prove that the distortion required to embed the integer lattice {0, 1, . ...