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Month: November 2016

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Algebraic general topology Filters General Topology

Generalized cofinite filters

By Victor Porton
On November 30, 2016

I have described generalized cofinite filters (including the “cofinite funcoid”). See the draft at http://www.mathematics21.org/binaries/addons.pdf

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#cofinite filter#Frechet filter
Algebraic general topology General Topology Open problems

A new diagram about funcoids and reloids

By Victor Porton
On November 26, 2016

Define for posets with order $latex \sqsubseteq$: $latex \Phi_{\ast} f = \lambda b \in \mathfrak{B}: \bigsqcup \{ x \in \mathfrak{A} \mid f x \sqsubseteq b \}$; $latex \Phi^{\ast} f = \lambda b \in \mathfrak{A}: \bigsqcap \{ x \in \mathfrak{B} \mid f x…

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#Galois connections
Algebraic general topology Filters General Topology

A new kind of product of funcoids

By Victor Porton
On November 4, 2016

The following is one of a few (possibly non-equivalent) definitions of products of funcoids: Definition Let $latex f$ be an indexed family of funcoids. Let $latex \mathcal{F}$ be a filter on $latex \mathrm{dom}\, f$. $latex a \mathrel{\left[ \prod^{[\mathcal{F}]} f \right]} b \Leftrightarrow…

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Algebraic general topology Filters General Topology Open problems

A different definition of product of funcoids

By Victor Porton
On November 2, 2016

Definition $latex a \mathrel{\left[ \prod^{(A 2)} f \right]} b \Leftrightarrow \exists M \in \mathrm{fin} \forall i \in (\mathrm{dom}\, f) \setminus M : \Pr^{\mathsf{RLD}}_i a \mathrel{[f_i]} \Pr^{\mathsf{RLD}}_i b$ for an indexed family $latex f$ of funcoids and atomic reloids $latex a$ and $latex…

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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
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    • Review
    • Publish
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