136 research outputs found
Fuzzy uniformities on function spaces
[EN] We study several uniformities on a function space and show that the fuzzy topology associated with the fuzzy uniformity of uniform convergence is jointly fuzzy continuous on Cf (X, Y ) ,the collection of all fuzzy continuous functions from a fuzzy topological space X into a fuzzy uniform space Y . We define fuzzy uniformity of uniform convergence on starplus-compacta and show that its corresponding fuzzy topology is the starplus-compact open fuzzy topology. Moreover, we introduce the notion of fuzzy equicontinuity and fuzzy uniform equicontinuity on fuzzy subsets of a function space and study their properties.Kohli, J.; Prasannan, A. (2006). Fuzzy uniformities on function spaces. Applied General Topology. 7(2):177-189. doi:10.4995/agt.2006.1922.SWORD1771897
An isomorphism of idempotent monads
We consider isomorphism between the idempotent measure monad based on the
maximum and the addition operations and the idempotent measure monad based on
the maximum and the multiplication operations. A one of the consequences of
this result is the construction of a fuzzy integral based on the maximum and
the addition operation. We also investigate convexities related to these
monads.Comment: arXiv admin note: text overlap with arXiv:2111.0661
Continuous selections of multivalued mappings
This survey covers in our opinion the most important results in the theory of
continuous selections of multivalued mappings (approximately) from 2002 through
2012. It extends and continues our previous such survey which appeared in
Recent Progress in General Topology, II, which was published in 2002. In
comparison, our present survey considers more restricted and specific areas of
mathematics. Note that we do not consider the theory of selectors (i.e.
continuous choices of elements from subsets of topological spaces) since this
topics is covered by another survey in this volume
Spaces of idempotent measures of compact metric spaces
We investigate certain geometric properties of the spaces of idempotent
measures. In particular, we prove that the space of idempotent measures on an
infinite compact metric space is homeomorphic to the Hilbert cube
- …