Garrido, Isabel; Meroño, Ana S.
[EN] The class of metric spaces (X,d) known as small-determined spaces, introduced by Garrido and Jaramillo, are properly defined by means of some type of real-valued Lipschitz functions on X. On the other hand, B-simple metric spaces introduced by Hejcman are defined in terms of some kind of bornologies of bounded subsets of X. In this note we present a common framework where both classes of metric spaces can be studied which allows us to see not only the relationships between them but also to obtain new internal characterizations of these metric properties.
We show that two possible definitions of sequential pseudocompactness are equivalent, and point out some consequences.[EN]
Bonanzinga, Maddalena; Cuzzupè, Maria Vittoria
[EN] In [A.V. Arhangel'skii and J. van Mill, On topological groups with a first-countable remainder, Top. Proc. 42 (2013), 157-163] it is proved that the character of a non-locally compact topological group with a first countable remainder doesn't exceed $\omega_1$ and a non-locally compact topological group of character $\omega_1$ having a compactification whose reminder is first countable is given. We generalize these results in the general case of an arbitrary infinite cardinal k.
Bosi, Gianni; Caterino, Alessandro; Ceppitelli, Rita
[EN] We study regular, normal and perfectly normal preorders by referring to suitable assumptions concerning the preorder and the topology of the space. We also present conditions for the existence of a countable continuous multi-utility representation, hence a Richter-Peleg multi-utility representation, by assuming the existence of a countable net weight.
Ekmekçi, Ramazan; Ertürk, Rıza
[EN] Graded ditopological texture spaces have been presented and discussed in categorical aspects by Lawrence M. Brown and Alexander Sostak (see bibliography). In this paper, the authors generalize the structure of difilters in ditopological texture spaces defined in (see bibliography) to the graded ditopological texture spaces and compare the properties of difilters and graded difilters.
Gupta, Ankit; Sarma, Ratna Dev
[EN] $(\lambda, \mu)$-regularity and $(\lambda, \mu)$-normality are defined for generalized topological spaces. Several variants of normality existing in the literature turn out to be particular cases of $(\lambda, \mu)$-normality. Uryshon's lemma and Titze's extension theorem are discussed in the light of ($\lambda, \mu$)-normality.
[EN] The purpose of this paper is to study the existence and location of fixed points for pseudo-contractive-type set-valued mappings in the setting of partial metric spaces by using Bianchini-Grundolfi gauge functions.