The paper is concerned with a very general version of Caristi’s coincidence theorem, in topological spaces (X, τ) satisfying some completeness conditions with respect to a function p : X ×X → [0,∞), and having as consequence Caristi’s fixed point theorem. The general result is applied to various concrete situations quasi-metric spaces, bornological spaces to obtain versions of Ekeland’s variati...

We define and study equivariant analytic and local cyclic homology for smooth actions of totally disconnected groups on bornological algebras. Our approach contains equivariant entire cyclic cohomology in the sense of Klimek, Kondracki and Lesniewski as a special case and provides an equivariant extension of the local cyclic theory developped by Puschnigg. As a main result we construct a multip...

For a $C^{*}$-category with strict $G$-action we construct examples of equivariant coarse homology theories. To this end first introduce versions Roe categories objects in $C^{*}$-categories which are controlled over bornological spaces, and then apply homological functor. These theories employed to verify that certain functors on the orbit category CP-functors. This fact has consequences for i...

Let A be an operator ideal on LCS’s. A continuous seminorm p of a LCS X is said to be A–continuous if Q̃p ∈ Ainj(X, X̃p), where X̃p is the completion of the normed space Xp = X/p−1(0) and Q̃p is the canonical map. p is said to be a Groth(A)–seminorm if there is a continuous seminorm q of X such that p ≤ q and the canonical map Q̃pq : X̃q −→ X̃p belongs to A(X̃q, X̃p). It is well-known that when A is the...

We study the relationships between Gateaux, Weak Hadamard and Fréchet differentiability and their bornologies for Lipschitz and for convex functions. AMS Subject Classification. Primary: 46A17, 46G05, 58C20. Secondary: 46B20.

1.2. The idea of quotient algebras was found, e.g. in [19], and the explicit descriptions, e.g. [3], based on Silva-differentiability on bornological vector spaces [2] produce a major impact in the field. The simplification [4] abandoned later in [5] indicates that a suitable framework of infinite dimensional differential calculus is definitely required. Our quick response with compact equicont...

We primarily make a general approach to the study of open covers and related selection principles using idea statistical convergence in metric space. In process we are able extend some results (Caserta et al. 2012; Chandra 2020) where bornological spaces have been investigated strong uniform (Beer Levi, 2009) on bornology. introduce notion statistical-Bs-cover, statistically-strong-B-Hurewicz s...