2,132 research outputs found
Fuzzy functions and an extension of the category L-Top of Chang-Goguen L-topological spaces
We study FTOP(L), a fuzzy category with fuzzy functions in the role of
morphisms. This category has the same objects as the category L-TOP of
Chang-Goguen L-topological spaces,but an essentially wider class of morphisms -
so called fuzzy functions introduced earlier in our joint work with U. Hohle
and H. Porst.Comment: 24 pages. This article will be revised and submitted for publication
elsewher
L-Fuzzy Semi-Preopen Operator in L-Fuzzy Topological Spaces
In this paper, we give the concept of L-fuzzy Semi-Preopen operator in
L-fuzzy topological spaces, and use them to score L-fuzzy SP-cmpactnness in
L-fuzzy topological spaces. We also study the relationship between L-fuzzy
SP-compactness and SP-compactness in L-topological spaces
On Abel statistical convergence
In this paper, we introduce and investigate a concept of Abel statistical
continuity. A real valued function is Abel statistically continuous on a
subset of , the set of real numbers, if it preserves Abel statistical
convergent sequences, i.e. is Abel statistically convergent
whenever is an Abel statistical convergent sequence of points in ,
where a sequence of point in is called Abel statistically
convergent to a real number if Abel density of the set is for every . Some other types
of continuities are also studied and interesting results are obtained.Comment: 11 pages. arXiv admin note: text overlap with arXiv:1101.144
Lowen type multi-fuzzy topological spaces
In this paper Lowen type multi-fuzzy topological space has been introduced
and characterization of topology by its nbd system is studied. Also the product
multi-fuzzy topological space has been introduced and it has been investigated
that 2nd countability and compactness are finitely productive in multi-fuzzy
topological spaces.Comment: 10 page
Generalizing Topology via Chu Spaces
By using the representational power of Chu spaces we define the notion of a
generalized topological space (or GTS, for short), i.e., a mathematical
structure that generalizes the notion of a topological space. We demonstrate
that these topological spaces have as special cases known topological spaces.
Furthermore, we develop the various topological notions and concepts for GTS.
Moreover, since the logic of Chu spaces is linear logic, we give an
interpretation of most linear logic connectives as operators that yield
topological spaces.Comment: This is paper that was written in 199
Soft N-Topological Spaces
Very recently, the idea of studying structures equipped with two or more soft
topologies has been considered by several researchers. Soft bitopological
spaces were introduced and studied, in 2014, by Ittanagi as a soft counterpart
of the notion of bitopological space and, independently, in 2015, by Naz,
Shabir and Ali. In 2017, Hassan too introduced the concept of soft
tritopological spaces and gave some first results. The notion of N-topological
space related to ordinary topological spaces was instead introduced and
studied, in 2011, by Tawfiq and Majeed. In this paper we introduce the concept
of Soft N-Topological Space as generalization both of the concepts of Soft
Topological Space and N-Topological Space and we investigate such class of
spaces and their basic properties with particular regard to their subspaces,
the parameterized families of crisp topologies generated by them and some new
separation axioms called N-wise soft T0, N-wise soft T1, and N-wise soft T2.Comment: 24 pages. arXiv admin note: text overlap with arXiv:1905.1305
Omitting uncountable types, and the strength of -valued logics
We study -valued logics that are closed under the
{\L}ukasiewicz-Pavelka connectives; our primary examples are the the continuous
logic framework of Ben Yaacov and Usvyatsov \cite{Ben-Yaacov-Usvyatsov:2010}
and the {\L}ukasziewicz-Pavelka logic itself. The main result of the paper is a
characterization of these logics in terms of a model-theoretic property,
namely, an extension of the omitting types theorem to uncountable languages
A Unified Theory on Some Basic Topological Concepts
Several mathematicians, including myself, have studied some unifications in
general topological spaces as well as in fuzzy topological spaces. For instance
in our earlier works, using operations on topological spaces, we have tried to
unify some concepts similar to continuity, openness, closedness of functions,
compactness, filter convergence, closedness of graphs, countable compactness
and Lindelof property. In this article, to obtain further unifications, we will
study -compactness and relations between -compactness,
filters and % -closure operator
A new variation on statistical ward continuity
A real valued function defined on a subset of , the set of
real numbers, is -statistically downward continuous if it preserves
-statistical downward quasi-Cauchy sequences of points in , where a
sequence of real numbers is called -statistically
downward quasi-Cauchy if for every , in
which is a non-decreasing sequence of positive real numbers
tending to such that ,
, and
for each positive integer . It turns out that a function is uniformly
continuous if it is -statistical downward continuous on an above bounded
set.Comment: 16 pages. arXiv admin note: text overlap with arXiv:1710.0051
Nets and Reverse Mathematics, a pilot study
Nets are generalisations of sequences involving possibly uncountable index
sets; this notion was introduced about a century ago by Moore and Smith. They
also established the generalisation to nets of various basic theorems of
analysis due to Bolzano-Weierstrass, Dini, Arzela, and others. More recently,
nets are central to the development of domain theory, providing intuitive
definitions of the associated Scott and Lawson topologies, among others. This
paper deals with the Reverse Mathematics study of basic theorems about nets. We
restrict ourselves to nets indexed by subsets of Baire space, and therefore
third-order arithmetic, as such nets suffice to obtain our main results. Over
Kohlenbach's base theory of higher-order Reverse Mathematics, the
Bolzano-Weierstrass theorem for nets implies the Heine-Borel theorem for
uncountable covers. We establish similar results for other basic theorems about
nets and even some equivalences, e.g. for Dini's theorem for nets. Finally, we
show that replacing nets by sequences is hard, but that replacing sequences by
nets can obviate the need for the Axiom of Choice, a foundational concern in
domain theory. In an appendix, we study the power of more general index sets,
establishing that the 'size' of a net is directly proportional to the power of
the associated convergence theorem.Comment: 34 pages, 1 figure, to appear in 'Computability
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