SEPARATING THE FAN THEOREM AND ITS WEAKENINGS

Separating the Fan Theorem and Its Weakenings

Varieties of the Fan Theorem have recently been developed in reverse constructive mathematics, corresponding to different continuity principles. They form a natural implicational hierarchy. Some of the implications have been shown to be strict, others strict in a weak context, and yet others not at all, using disparate techniques. Here we present a family of related Kripke models which suffices...

Separating the Fan Theorem and Its Weakenings II

Varieties of the Fan Theorem have recently been developed in reverse constructive mathematics, corresponding to different continuity principles. They form a natural implicational hierarchy. Earlier work showed all of these implications to be strict. Here we re-prove one of the strictness results, using very different arguments. The technique used is a mixture of realizability, forcing in the gu...

Fan-KKM Theorem in Minimal Vector Spaces and its Applications

In this paper, after reviewing some results in minimal space, some new results in this setting are given. We prove a generalized form of the Fan-KKM typetheorem in minimal vector spaces. As some applications, the open type of matching theorem and generalized form of the classical KKM theorem in minimal vector spaces are given.

fan-kkm theorem in minimal vector spaces and its applications

in this paper, after reviewing some results in minimal space, some new results in this setting are given. we prove a generalized form of the fan-kkm typetheorem in minimal vector spaces. as some applications, the open type of matching theorem and generalized form of the classical kkm theorem in minimal vector spaces are given.

The fan theorem