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Month: January 2014

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Algebraic general topology General Topology Open problems

Conjecture: Connectedness in proximity spaces

By Victor Porton
On January 18, 2014

I’ve asked this question at math.StackExchange.com Let $latex \delta$ be a proximity. A set $latex A$ is connected regarding $latex \delta$ iff $latex \forall X,Y \in \mathscr{P} A \setminus \{ \emptyset \} : \left( X \cup Y = A \Rightarrow X \mathrel{\delta}…

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Algebraic general topology Category theory General Topology

On a common generalization of funcoids and reloids

By Victor Porton
On January 16, 2014

Just a few seconds ago I had an idea how to generalize both funcoids and reloids. Consider a precategory, whose objects are sets product $latex \times$ of filters on sets ranging in morphisms of this category operations $latex \mathrm{dom}$ and $latex \mathrm{im}$…

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Algebraic general topology General Topology Open problems

Conjecture about funcoids proved

By Victor Porton
On January 14, 2014

I’ve proved this my conjecture: $latex g \circ f = \bigsqcap \left\{ G \circ F \,|\, F \in \mathrm{up}\, f, G \in \mathrm{up}\, g \right\}$ for every composable funcoids $latex f$ and $latex g$. See my book (in the current draft the…

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Algebraic general topology Filters General Topology Publications

An error in my book

By Victor Porton
On January 12, 2014

In the draft of my book there was an error. I’ve corrected it today. Wrong: $latex \forall a, b \in \mathfrak{A}: ( \mathrm{atoms}\, a \sqsubset \mathrm{atoms}\, b \Rightarrow a \subset b)$. Right: $latex \forall a, b \in \mathfrak{A}: ( a \sqsubset b…

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#IJPAM#International Journal of Pure and Applied Mathematics
Filters

A filter which cannot be partitioned into ultrafilters

By Victor Porton
On January 4, 2014

I’ve proved: There exists a filter which cannot be (both weakly and strongly) partitioned into ultrafilters. It is an easy consequence of a lemma proved by Niels Diepeveen (also Karl Kronenfeld has helped me to elaborate the proof). See the preprint of…

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#partition#ultrafilters
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  • SCIENCE
  • Home
  • Algebraic General Topology
  • Axiomatic Theory of Formulas
  • Limit of a Discontinuous Function
  • More
  • Prize
  • SCIENCE
  • Home
    • Blog
    • Soft
  • Algebraic General Topology
    • Paperback
    • Ebook
    • PDF
  • Axiomatic Theory of Formulas
    • Paperback
    • Ebook
    • PDF
  • Limit of a Discontinuous Function
  • More
    • Donate
    • Review
    • Publish
    • Politics
  • Prize