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Month: May 2013

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Algebraic general topology General Topology

New chapter in my research monograph

By Victor Porton
On May 31, 2013

I’ve added new chapter 11 “Total boundness of reloids” to my book “Algebraic General Topology. Volume 1”. It expresses several kinds of boundness of reloids, which are however the same total boundness in the special case of uniform spaces.

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Algebraic general topology General Topology

Change of terminology

By Victor Porton
On May 30, 2013

I realized that the terms “discrete funcoid” and “discrete reloid” conflict with conventional usage of “discrete topology” and “discrete uniformity”. Thus I have renamed them into “principal funcoid” and “principal reloid”. See my research monograph.

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Algebraic general topology General Topology

Totally bounded reloids, a generalization of totally bounded uniform spaces

By Victor Porton
On May 25, 2013

This is a straightforward generalization of the customary definition of totally bounded sets on uniform spaces: Definition Reloid $latex f$ is totally bounded iff for every $latex E \in \mathrm{GR}\, f$ there exists a finite cover $latex S$ of $latex \mathrm{Ob}\, f$…

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Algebraic general topology General Topology

“Simple product”, a new kind of product of funcoids

By Victor Porton
On May 22, 2013

Today I’ve discovered a new kind of product of funcoids which I call “simple product”. It is defined by the formulas $latex \left\langle \prod^{(S)}f \right\rangle x = \lambda i \in \mathrm{dom}\, f: \langle f_i \rangle x_i$ and $latex \left\langle \left( \prod^{(S)}f \right)^{-1}…

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Filters Math on the Web Open problems

A partial proof of “Partitioning a filter into ultrafilters” conjecture

By Victor Porton
On May 1, 2013

I’ve put a partial partial proof of “Every filter on a set can be strongly partitioned into ultrafilters” conjecture at PlanetMath. Please collaborate in solving this conjecture.

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  • SCIENCE
  • Home
  • Algebraic General Topology
  • Axiomatic Theory of Formulas
  • Discontinuous Analysis
  • More
  • Prize
  • SCIENCE
    • Journal with post-moderation
    • World Science DAO
  • Home
    • Blog
    • Soft
  • Algebraic General Topology
    • Paperback
    • Ebook
    • PDF
  • Axiomatic Theory of Formulas
    • Paperback
    • Ebook
    • PDF
  • Discontinuous Analysis
    • Full Course
  • More
    • Donate
    • Review
    • Publish
    • Politics
  • Prize