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Month: May 2018

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Algebraic general topology Category theory General Topology

I proved that certain functors between topological spaces and endofuncoid are adjoint

By Victor Porton
On May 25, 2018

I proved: Theorem $latex T$ is a left adjoint of both $latex F_{\star}$ and $latex F^{\star}$, with bijection which preserves the “function” part of the morphism. The details and the proof is available in the draft of second volume of my online book. The…

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Algebraic general topology Filters General Topology

A counterexample to my recent conjecture

By Victor Porton
On May 20, 2018

After proposing this conjecture I quickly found a counterexample: $latex S = \left\{ (- a ; a) \mid a \in \mathbb{R}, 0 < a < 1 \right\}$, $latex f$ is the usual Kuratowski closure for $latex \mathbb{R}$.

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Algebraic general topology Filters General Topology Open problems

New conjecture about funcoids

By Victor Porton
On May 20, 2018

Conjecture $latex \langle f \rangle \bigsqcup S = \bigsqcup_{\mathcal{X} \in S} \langle f \rangle \mathcal{X}$ if $latex S$ is a totally ordered (generalize for a filter base) set of filters (or at least set of sets).

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Algebraic general topology Category theory General Topology Open problems

Mappings between endofuncoids and topological spaces

By Victor Porton
On May 18, 2018

I started research of mappings between endofuncoids and topological spaces. Currently the draft is located in volume 2 draft of my online book. I define mappings back and forth between endofuncoids and topologies. The main result is a representation of an endofuncoid…

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Algebraic general topology Filters General Topology Open problems

Expressing limits as implications

By Victor Porton
On May 3, 2018

I have added to my book section “Expressing limits as implications”. The main (easy to prove) theorem basically states that $latex \lim_{x\to\alpha} f(x) = \beta$ when $latex x\to\alpha$ implies $latex f(x)\to\beta$. Here $latex x$ can be taken an arbitrary filter or just…

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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