scholarly journals T_4, Urysohn's Lemma, and Tietze Extension Theorem for Constant Filter Convergence Spaces

2021 ◽  
Keyword(s):  
Extension Theorem ◽  
Convergence Spaces ◽  
Filter Convergence

scholarly journals Probabilistic convergence spaces

1996 ◽  
Vol 61 (3) ◽  
pp. 400-420 ◽  
Author(s):  
G. D. Richardson ◽  
D. C. Kent
Keyword(s):  
Basic Theory ◽  
Convergence In Probability ◽  
Previous Theory ◽  
Convergence Spaces ◽  
Convergence Almost Everywhere ◽  
Almost Everywhere ◽  
Filter Convergence

AbstractA basic theory for probabilistic convergence spaces based on filter convergence is introduced. As in Florescu's previous theory of probabilistic convergence structures based on nets, one is able to assign a probability that a given filter converges to a given point. Various concepts and theorems pertaining to convergence spaces are extended to the realm of probabilistic convergence spaces, and illustrated by means of examples based on convergence in probability and convergence almost everywhere. Diagonal axioms due to Kowalsky and Fischer are also studied, first for convergence spaces and then in the setting of probabilistic convergence spaces.

scholarly journals A note on separation and compactness in categories of convergence spaces

2003 ◽  
Vol 4 (1) ◽  
pp. 1 ◽  
Author(s):  
Mehmet Baran ◽  
Muammer Kula
Keyword(s):  
Topological Category ◽  
Convergence Spaces ◽  
Filter Convergence

<p>In previous papers, various notions of compact, T<sub>3</sub>, T<sub>4</sub>, and Tychonoff objects in a topological category were introduced and compared. The main objective of this paper is to characterize each of these classes of objects in the categories of filter and local filter convergence spaces as well as to examine how these various generalizations are related.</p>

scholarly journals Local T_3 Constant Filter Convergence Spaces

2020 ◽  
Vol 33 (2) ◽  
pp. 446-454
Author(s):  
Ayhan ERCİYES ◽  
Tesnim Meryem BARAN
Keyword(s):  
Convergence Spaces ◽  
Filter Convergence

Relativized realizability in intuitionistic arithmetic of all finite types

1978 ◽  
Vol 43 (1) ◽  
pp. 23-44 ◽  
Author(s):  
Nicolas D. Goodman
Keyword(s):  
Extension Theorem ◽  
General Notion ◽  
Conservative Extension ◽  
First Order ◽  
New Information ◽  
Reflection Theorem ◽  
Order Arithmetic ◽  
Special Case ◽  
Dependent Choice ◽  
Intuitionistic Arithmetic

In this paper we introduce a new notion of realizability for intuitionistic arithmetic in all finite types. The notion seems to us to capture some of the intuition underlying both the recursive realizability of Kjeene [5] and the semantics of Kripke [7]. After some preliminaries of a syntactic and recursion-theoretic character in §1, we motivate and define our notion of realizability in §2. In §3 we prove a soundness theorem, and in §4 we apply that theorem to obtain new information about provability in some extensions of intuitionistic arithmetic in all finite types. In §5 we consider a special case of our general notion and prove a kind of reflection theorem for it. Finally, in §6, we consider a formalized version of our realizability notion and use it to give a new proof of the conservative extension theorem discussed in Goodman and Myhill [4] and proved in our [3]. (Apparently, a form of this result is also proved in Mine [13]. We have not seen this paper, but are relying on [12].) As a corollary, we obtain the following somewhat strengthened result: Let Σ be any extension of first-order intuitionistic arithmetic (HA) formalized in the language of HA. Let Σω be the theory obtained from Σ by adding functionals of finite type with intuitionistic logic, intensional identity, and axioms of choice and dependent choice at all types. Then Σω is a conservative extension of Σ. An interesting example of this theorem is obtained by taking Σ to be classical first-order arithmetic.

The Tietze Extension Theorem and the Open Mapping Theorem

1986 ◽  
Vol 93 (3) ◽  
pp. 190-191 ◽  
Author(s):  
Sandy Grabiner
Keyword(s):  
Extension Theorem ◽  
Open Mapping ◽  
Open Mapping Theorem

scholarly journals Hopf Extension Theorem of Measure

2009 ◽  
Vol 17 (2) ◽  
Author(s):  
Noboru Endou ◽  
Hiroyuki Okazaki ◽  
Yasunari Shidama
Keyword(s):  
Extension Theorem

A biregular extension theorem from a fractal surface in

2011 ◽  
Vol 18 (1) ◽  
pp. 21-29
Author(s):  
Ricardo Abreu Blaya ◽  
Juan Bory Reyes ◽  
Tania Moreno García
Keyword(s):  
Continuous Function ◽  
Bounded Domain ◽  
Extension Theorem ◽  
Fractal Surface ◽  
Fractal Boundary ◽  
Hölder Continuous

Abstract The aim of this paper is to prove the characterization on a bounded domain of with fractal boundary and a Hölder continuous function on the boundary guaranteeing the biregular extendability of the later function throughout the domain.

scholarly journals Cartesian-closedness and subcategories of (L, M)-fuzzy Q-convergence spaces

2021 ◽  
Author(s):  
Bin Pang ◽  
Lin Zhang
Keyword(s):  
Convergence Spaces ◽  
Cartesian Closedness

Epis in categories of convergence spaces

1993 ◽  
Vol 61 (3-4) ◽  
pp. 195-201 ◽  
Author(s):  
D. Dikranjan ◽  
E. Giuli
Keyword(s):  
Convergence Spaces

A SUFFICIENT AND NECESSARY CONDITION FOR CREDIBILITY MEASURES

2006 ◽  
Vol 14 (05) ◽  
pp. 527-535 ◽  
Author(s):  
XIANG LI ◽  
BAODING LIU
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Extension Theorem ◽  
The Self ◽  
Necessary Condition ◽  
Self Duality ◽  
Duality Property ◽  
Sufficient And Necessary Condition

Possibility measures and credibility measures are widely used in fuzzy set theory. Compared with possibility measures, the advantage of credibility measures is the self-duality property. This paper gives a relation between possibility measures and credibility measures, and proves a sufficient and necessary condition for credibility measures. Finally, the credibility extension theorem is shown.

Sign in / Sign up

Export Citation Format

Share Document