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, […]
Connectors and generalized connectedness – preprint
I sent the preprint of the article Connectors and generalized connectedness to Topology and its Applications journal. I’m not sure they will classify my article as topological. If not I’ll send to an other journal.
“Connectors and generalized connectedness” online article
I released the first draft not marked preliminary (that is supposedly readable by mathematicians) of my article Connectors and generalized connectedness. I need yet to little polish it and check for errors to make it a preprint before I’ll send it to a math journal. But I think you may read it now.
Connectors and generalized connectedness – draft
I updated online draft of the article “Connectors and generalized connectedness” which considers a generalization of topological connectedness, graph connectedness, proximal connectedness, uniform connectedness, etc.
Draft about connectedness
I put online a preliminary draft of my article Connectors and generalized connectedness. This preliminary draft is yet unreadable. The primary reason why I put this unreadable preliminary draft online is that I want to refer to it from this MathOverflow question. From the article: This article is an unreadable preliminary draft. Some definitions and […]
A distributive law for filter objects
I recently proved the following conjecture (now a theorem): Theorem $latex A\cap^{\mathfrak{F}}\bigcup{}^{\mathfrak{F}}S = \bigcup{}^{\mathfrak{F}} \{ A\cap^{\mathfrak{F}} X | X\in S \}$ for every set $latex A\in\mathscr{P}\mho$ and every $latex S\in\mathscr{P}\mathfrak{F}$ where $latex \mathfrak{F}$ is the set of filter objects on some set $latex \mho$. This theorem is a direct consequence of the following lemma: Lemma […]