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A Generalized Mazur-Ulam Theorem for Fuzzy Normed Spaces
(Hindawi Publishing Corporation, 2014-06-02)
We introduce fuzzy norm-preserving maps, which generalize the concept of fuzzy isometry. Based on the ideas from Vogt, 1973,
and V¨ais¨al¨a, 2003, we provide the following generalized version of theMazur-Ulam theorem in ...
An identification theorem for the completion of the Hausdorff fuzzy metric
(Elsevier, 2013)
We prove that given a fuzzy metric space (in the sense of Kramosil and Michalek), the completion of its Hausdorff fuzzy metric space is isometric to the Hausdorff fuzzy metric space of its completion, when the Hausdorff ...
Totally Lindelöf and totally ω-narrow paratopological groups
(Elsevier, 2008-01)
In many natural objects of topological algebra that possess the algebraic structure of a group, the operations of
inversion and multiplication are not necessarily continuous—it suffices to recall the groups of homeomorphisms
of ...
Fuzzy uniform structures and continuous t-norms
(Elsevier, 2010)
We introduce and discuss a notion of fuzzy uniform structure that provides a direct link with the classical theory of uniform spaces. More exactly, for each continuous t-norm we prove that the category of all fuzzy uniform ...
R-factorizable paratopological groups
(Elsevier, 2010)
For i = 1, 2, 3, 3.5, we define the class of R<sub>i</sub>-factorizable paratopological groups G by the condition that every continuous real-valued function on G can be factorized through a continuous homomorphism p : G → ...
On the construction of domains of formal balls for uniform spaces
(2014-05)
In the spirit of the well-known constructions of Edalat and Heckmann for metric spaces, we endow the set of formal (closed) balls of a given uniform space with a structure of poset and prove several of its properties, which ...
Dimension and entropy in compact topological groups
(Elsevier, 2019-03)
We study the topological entropy h(f) of continuous endomorphisms f of compact-like groups. More specifically, we consider the e-spectrum E top (K) for a compact-like group K (namely, the set of all values h(f) , when f ...
Spaces splittable over the class of Eberlein and descriptive compact spaces
(Springer Milan, 2018)
We study splittability over some classes of compact spaces which are useful in functional analysis and general topology. Among other things we show that a scattered pseudocompact space splittable over the class of Eberlein ...
Some questions about Zadeh's extension on metric spaces
(Elsevier, 2018-10-29)
For
a
continuous
function
f
on
a
Hausdorff
space
X
,
we
prove
that
[
̂
f(u)
]
α
=
f(u
α
)
for
each
u
∈
F
(X)
and
α
∈[
0
,
1
]
,
where
̂
f
is
the
Zadeh’s
extension
of
f
.
By
...
Constructive approximation of level continuous fuzzy functions 1
(IOS, 2019-06)
We consider the space of continuous functions defined between a locally compact Hausdorff space and the space of fuzzy numbers endowed with the level convergence topology. We obtain a Stone-Weierstrass type theorem for ...