A topological central point theorem

A fixed point theorem in a Hausdorff topological vector space

In this paper, we will give a new fixed point theorem for lower semicontinuous multimaps in a Hausdorff topological vector space.

Torelli's Theorem from the Topological Point of View

Caristi Type Coincidence Point Theorem in Topological Spaces

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...

A Topological Minimax Theorem

We present a topological minimax theorem (Theorem 2.2). The topological assumptions on the spaces involved are somewhat weaker than those usually found in the literature. Even when reinterpreted in the convex setting of topological vector spaces, our theorem yields nonnegligible improvements, for example, of the Passy–Prisman theorem and consequently of the Sion theorem, contrary to most result...

A topological completeness theorem

We prove a topological completeness theorem for innnitary geometric theories with respect to sheaf models. The theorem extends a classical result of Makkai and Reyes, stating that any topos with enough points has an open spatial cover. We show that one can achieve in addition that the cover is connected and locally connected.