Related papers: A remark on the paper "Redundancy of multiset topo…
In this paper, we prove the redundancies of multiset topologies. It is shown that there is a complement preserving isomorphism between $(P^\star(U),\sqsubseteq)$ and $(\mathcal{P}(X\times\mathbb{N}),\subseteq)$. It therefore follows that…
Here we give a reformulation of a key lemma in the paper [2], "Spaces of Topological Complexity One", which is necessary due to an oversight.
In this paper we make some observations concerning m-metric spaces and point out some discrepancies in the proofs found in the literature. To remedy this, we propose a new topological construction and prove that it is in fact a…
A generalization of metric space is presented which is shown to admit a theory strongly related to that of ordinary metric spaces. To avoid the topological effects related to dropping any of the axioms of metric space, first a new, and…
Several recent papers in digital topology have sought to obtain fixed point results by mimicking the use of tools from classical topology, such as complete metric spaces. We show that in many cases, researchers using these tools have…
Several recent papers in digital topology have sought to obtain fixed point results by mimicking the use of tools from classical topology, such as complete metric spaces and homotopy invariant fixed point theory. We show that in many cases,…
This paper has been withdrawn due to a crucial error in the proof of the main theorem
We continue the work of [5] and [3], in which are considered papers in the literature that discuss fixed point assertions in digital topology. We discuss published assertions that are incorrect or incorrectly proven; that are severely…
This paper has been withdrawn by the authors due to a mistake in the proof of the chief result. In particular Theorem 1.3 is correct, while Theorem 1.1 and Theorem 1.2 hold with \mu>0 and a suitable restriction on the exponent p. The proof…
This article has been withdrawn due to an error in a proof of the main result.
This paper continues a series discussing flaws in published assertions concerning fixed points in digital metric spaces.
We discuss published assertions concerning fixed points in digital metric spaces that are incorrect or incorrectly proven, or reduce to triviality.
This paper has been withdrawn by the authors due to a crucial error.
Consider a set represented by an inequality. An interesting phenomenon which occurs in various settings in mathematics is that the interior of this set is the subset where strict inequality holds, the boundary is the subset where equality…
This paper has been removed by the author due to a misstatement in Theorem 1 and a gap in its proof. A corrected and largely extended successor (a joint work with Thomas Bauer and Tomasz Szemberg) can be found under math.AG/0312211,
In our previous work "Characterization of certain homorphic geodesic cycles on Hermitian locally symmetric manifolds of the noncompact type" in "Modern methods in Complex Analysis" Annals of Math. Studies 138 (1995) 85-118, we formulated a…
In this paper, we generalize an elementary real-analysis result to a class of topological vector spaces. We also give an example of a topological vector space to which the result cannot be generalized.
We describe an error in the proof of a key proposition, which was necessary for the proof of the main result. Alternate proofs of the main result are given by Ozsvath-Stipsicz-Szabo and Dai-Hom-Stoffregen-Truong.
We provide further explanation of the significance of a construction in a recent paper of Wolf [Israel J. Math. 179 (2010), 253-278] in the context of the problem of finding large subspaces in sumsets.
The paper introduces the class of O-metric spaces, a novel generalization of metric-type spaces, classifying almost all possible metric types into upward and downward O-metrics. We list some topologies arising from O-metrics and discuss…