A fiber homotopy extension theorem

A FUZZY VERSION OF HAHN-BANACH EXTENSION THEOREM

In this paper, a fuzzy version of the analytic form of Hahn-Banachextension theorem is given. As application, the Hahn-Banach theorem for$r$-fuzzy bounded linear functionals on $r$-fuzzy normedlinear spaces is obtained.

A Borsuk Theorem on Homotopy Types

We present a Borsuk’s theorem published first in [3] (compare also [4, pages 119–120]). It is slightly generalized, the assumption of metrizability is omitted. We introduce concepts needed for the formulation and the proof of theorems on upper semi-continuous decompositions, retracts, strong deformation retract. However, only those facts that are necessary in the proof have been proved.

A Homotopy Theorem for Matroids, Ii

A Torus Theorem for Homotopy Nilpotent Groups

Nilpotency for discrete groups can be defined in terms of central extensions. In this paper, the analogous definition for spaces is stated in terms of principal fibrations having infinite loop spaces as fibers, yielding a new invariant we compare with classical cocategory, but also with the more recent notion of homotopy nilpotency introduced by Biedermann and Dwyer. This allows us to character...

A Homotopy Theorem for Matroids, I