6,084 research outputs found
Groups with a small set of generators
No full textThe combinatorial notion of a "small set" in an abstract group was introduced by Bella and Malykhin. Then Malykhin and Moresco proved that some infinite abelian groups admit a small set of generators and raised the problem of establishing that all groups have a small set of generators. The present paper provides many classes of groups where the problem can be resilved in the positive
Audiomobiles, Sculptures and Conundrums
No full textRoberto Gerhard was a pioneer of electronic music in England creating a number of substantial concert, theatre and radio works from as early as 1954. Gerhard’s electronic music is one of the richest repositories for understanding the development of the composer’s late compositional technique. Apart from the Symphony no.3, ‘Collages’, none of Gerhard’s electronic music is published. This paper will discuss aspects of Gerhard’s electronic music, focusing on Audiomobiles (1958-59) and Sculptures (1963)
On the fuzzes which are complete rings of sets
No full textObjects in the category of fuzzes whose underlying set is a complete ring of sets are described as subdirect products of particular elementar objects
alpha-star-compactness of the fuzzy unit interval
No full textAnswering a question raised by Gantner, Steinlage and Warren, we provide some conditions for the alpha-star-compactness of the fuzzy unit interval
-additive topological spaces
No full textWe investigate omega_mu-additive topological spaces, introduced by B. Sikorski, and related topics such as omega_mu-product topology, omega_mu-compactness, omega_mu-uniformity, and obtain some significant improvements of existing results
Some Results on omega_mu-metric spaces
No full textSome concepts used in valued spaces (spherical completeness and closure, pseudo-convergence) are introduced in the study of omega_mu-metric spaces; in this context such notions are discussed and employed to show some extensions of theorems well-known in metric spaces (contraction lemma, Baire's theorem, embedding of the generalized Cantor space)
Fuzzy proximities compatible with Lowen Fuzzy uniformities
No full textWe introduce a notion of fuzzy proximity which behaves well with respect to the fuzzy uniformities introduced by R. Lowen and prove some related results. We also provide some critical remarks about fuzzy topologies, fuzzy proximities and fuzzy uniformities
Some omega_mu-metrization theorems
No full textWe give a necessary and sufficient condition for a topological space to be omega_mu-metrizable (i.e. it admits a uniformity with a linearly ordered base of ccofinality omega_mu). This characterization, which extends a classic result of R.H. Bing, leads us to prove that the omega_mu-additive spaces which are either linearly ordered or omega_mu-compact are omega_mu-metrizable iff their diagonal is the intersection of a family of omega_mu-many open sets
On fuzzy metrizability
No full textWe answer two questions raised by M. A. Erceg [J. Math. Anal. Appl. 69 (1979), 205-230]: precisely we show that the fuzzy unit interval is never T0, except in the standard case, and that a fuzzy pseudo-metrizable T0 space is metrizable in the sense of Erceg (ibid.). Hence the two definitions of metrizable space given in B. Hutton and I. Reilly [Fuzzy Sets and Systems 3 (1980), 93-104] and Erceg (ibid.) are equivalent
Fuzzy uniformities induced by fuzzy proximities
No full textGiven a fuzzy proximity δ, we construct a fuzzy uniformity (in the sense of Lowen) which turns out to be the coarse stone among those which induce δ. We show that some basic theorems of general topology about precompact uniformities have a nice extension to fuzzy set topology
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