Funcoids and Reloids updated
I updated the the online draft of “Funcoids and Reloids” article. This is almost ready preprint (which I will be able to submit after I will have “Filters on Posets and Generalizations” published). The most notable change in this edition is corrected an error in the proof of the theorem which characterizes monovaluedness of funcoids. […]
Two open problems about completion of funcoids and reloids
In Funcoids and Reloids online article I added two new open problems: 1. $latex \mathrm{Compl} f = f \setminus^{\ast \mathsf{FCD}} (\Omega\times^{\mathsf{FCD}} \mho)$ for every funcoid $latex f$? 2. $latex \mathrm{Compl} f = f \setminus^{\ast \mathsf{RLD}} (\Omega\times^{\mathsf{RLD}} \mho)$ for every reloid $latex f$?
Funcoids and Reloids – updated
My online article Funcoids and Reloids as well as my list of open problems are updated. Added two open problems: 1. $latex (\mathsf{RLD})_{\mathrm{in}}$ is not a lower adjoint (in general)? 2. $latex (\mathsf{RLD})_{\mathrm{out}}$ is neither a lower adjoint nor an upper adjoint (in general)? Also added an example proving that “$latex (\mathsf{FCD})$ does not preserve […]
Funcoids and Reloids – updated
My online draft article Funcoids and Reloids updated with minor changes in “Connectedness regarding funcoids and reloids” section.
Article sent to Rejecta
As I wrote before my preprint Connectors and generalized connectedness was rejected, saying that I do not relate it with existing research. I decided to sent the manuscript to Rejecta Mathematica. I submitted it to Rejecta Mathematica yesterday. Previously I was going to study category theory and then rewrite my article in order to resubmit […]
Two new open problems about relationships of funcoids and reloids
In the past I overlooked the following two open problems considering them obvious. When I tried to write proofs of these statements down I noticed these are not trivial. So I added them to my list of open problems. Question $latex (\mathsf{RLD})_{\mathrm{out}} ( \mathcal{A} \times^{\mathsf{FCD}} \mathcal{B}) = \mathcal{A} \times^{\mathsf{RLD}} \mathcal{B}$ for every filter objects $latex […]
A counter-example against a distributivity law for funcoids
Example There exist funcoids $latex {f}&fg=000000$ and $latex {g}&fg=000000$ such that $latex \displaystyle ( \mathsf{RLD})_{\mathrm{out}} (g \circ f) \neq ( \mathsf{RLD})_{\mathrm{out}} g \circ ( \mathsf{RLD})_{\mathrm{out}} f. &fg=000000$ Proof: Take $latex {f = {( =)} |_{\Omega}}&fg=000000$ and $latex {g = \mho \times^{\mathsf{FCD}} \left\{ \alpha \right\}}&fg=000000$ for some $latex {\alpha \in \mho}&fg=000000$. Then $latex {( \mathsf{RLD})_{\mathrm{out}} f […]
Question: Will publishing in Rejecta hinder further publication?
My manuscript Connectors and generalized connectedness sent to Topology and its Applications math journal was rejected saying that I have not cited enough articles in order to show that the terminology I introduced and my results are novel, not re-discovery of others’ results just using a different terminology. The reviewer has suggested me to read […]
I consent with rejection of my article
My submission of my Connectors and Generalized Connectedness math article was rejected due a reviewer saying that the author (that is I) must go through the literature and find sources for general connectedness (e.g. Athangelskii+Wiegandt, Castellini, Herrlich, Petz, Preuss, Lowen, …..) That is I was rejected due not enough references and links with existing literature […]
How connectedness is related with continuity?
I sent my article Connectors and generalized connectedness to a math journal for peer review and publication. This my article however does not address an important facet: It is well known that a set is connected if every function from it to a discrete space is constant. AFAIK, this holds for topological connectedness and continuity, […]