Soft topology studies a structure on the collection of all soft sets on a given set of alternatives (the relevant attributes being fixed). It is directly inspired by the axioms of a topological ...space. This paper contributes to the theoretical bases of soft topology in various ways. We extend a general construction of soft topologies from topologies on the set of alternatives in two different directions. An extensive discussion with criteria about what a soft counterpart of “topological separability” should satisfy is also given. The interactions of the properties that arise with separability, and of second-countability and its soft counterpart, are studied under the general mechanisms that generate soft topological spaces. The first non-trivial examples of soft second-countable soft topological spaces are produced as a consequence.
Using animate nouns to refer to entities in the world involves a complex interaction of ontology, cognition and language. The present study evaluates two accounts of the use of animate nouns, with ...Mandarin Chinese as the vehicle for testing between the competing accounts. One account was proposed by Cheng et al. (2008. How universal is the Universal Grinder? In Marjo van Koppen & Bert Botma (eds.),
, 50–62. Amsterdam & Philadelphia: John Benjamins). These researchers contend that the count interpretation is basic for Mandarin animate nouns, due to a lexical blocking effect. To access the alternative, mass interpretation requires some kind of pragmatic coercion. A second account was proposed by Pelletier, based on English (1975. Non-Singular reference: Some preliminaries.
5(4). 451–465; 2012. Lexical nouns are both +MASS and +COUNT, but they are neither +MASS nor + COUNT. In Diane Massam (ed.),
, 9–26. Oxford: Oxford University Press). We extend this account to Mandarin animate nouns, proposing that they are encoded in the mental lexicon with both a count sense and a mass sense. To adjudicate between the accounts, we conducted four experiments that were designed to assess the interpretation assigned to animate nouns by Mandarin-speaking children and adults. The experimental conditions manipulated both the syntactic structures of the sentences and the non-linguistic contexts in which those sentences were presented. The experimental findings support our proposal that both mass and count interpretations of animate nouns are available to children and adults when sentences are presented in contexts that are congruent with these interpretations. The findings also suggest that syntactic structure is an even more critical factor in determining the interpretation that is assigned to animate nouns in Mandarin.
Countability is a universal lexical category that provides a binary division of nouns into countable anduncountable nouns or is also called count and mass nouns. Usually, count nouns refer to things ...or objectswhich can be individuated and thus counted, while mass nouns refer to substances or stuff such as water,wine, blood, or mud for which it is less easy to identify what and how to count. This cognitive divisionleaves abstract nouns out. Abstract nouns neither refer to things or objects nor to substances or stuff. Onthe contrary, the reference of abstract nouns is rather heterogeneous comprising different kinds of nounssuch as processes, states, events, measure and time terms, and alike. The aim of this paper is to presentthe challenges abstract nouns pose for theories of countability, and to reflect on possibilities toincorporate abstract nouns in contemporary theories of countability. The research discussed in this papercircles around English abstract nouns but we will also discuss the application of certain semanticphenomena onto Bosnian nouns.
In this paper, we investigate weak countability axioms of coset spaces. We first discuss biradial coset spaces. It is mainly shown that if H is a closed neutral subgroup of a topological group G, ...then (1) G/H is biradial ⇔ G/H is nested; (2) G/H is monotonically normal if G/H is nested; (3) G/H is metrizable ⇔ G/H is a biradial space with countable pseudocharacter. We also study coset spaces with certain point-countable covers. In particular, we prove that if H is a closed neutral subgroup of a topological group G, then (4) G/H is metrizable ⇔ G/H is determined by a point-finite cover consisting of bisequential spaces. In the end, we consider coset spaces with certain local countable networks. It is mainly shown that if H is a closed neutral subgroup of a topological group G, then (5) G/H is metrizable ⇔ G/H is an α4 and k-space with an ωω-base; (6) G/H is cosmic ⇔ G/H is a separable space with countable cn-character; (7) G/H is metrizable ⇔ G/H has countable cn-character provided G/H has the Baire property.
Portioning-out and individuation are two important semantic properties for the characterization of countability. In Mandarin, nouns are not marked with count-mass syntax, and it is controversial ...whether individuation is encoded in classifiers or in nouns. In the present study, we investigates the interpretation of a minimal pair of non-interrogative
-pronominal phrases, including
-N and
-N. Due to the presence/absence of the individual classifier
, these two
-pronominal phrases differ in how they encode portioning-out and individuation. In two experiments, we used a Truth Value Judgment Task to examine the interpretation of these two
-pronominal phrases by Mandarin-speaking adults and 4-to-6-year-old children. We found that both adults and children are sensitive to their interpretative differences with respect to the portioning-out and individuation properties. They assign either count or mass readings to the bare
-pronominal phrase
-N depending on specific contexts, but only count readings to the classifier-bearing
-pronominal phrase
-N. Moreover, the portioning-out and individuation properties associated with the individual classifier
emerge independently in the course of language development, with the portioning-out property taking precedence over the individuation property. Taken together, the present study provides new evidence for the view that the portioning-out and individuation properties in Mandarin are encoded in classifiers rather than in nouns, and these two semantic properties are two distinct components in our grammar.
In this note, we will prove that if H is a closed strong subgyrogroup of a strongly topological gyrogroup G and H is neutral, then (1) G/H is completely regular; (2) G/H is metrizable if and only if ...it is first-countable; (3) G/H is submetrizable if and only if it has countable pseudocharacter; (4) G/H is metrizable if and only if it is a bisequential space. In addition, if H is a compact L-subgyrogroup of a topological gyrogroup G, then each compact subspace of G/H is first-countable if and only if every compact subspace of G/H is metrizable.
We will consider soft topologies defined on the same universe
X
with
E
as the set of parameters. It is shown that soft topologies are not equivalent to the general topologies defined on
X
. Moreover, ...some implications between soft separating axioms are different than those for ordinary topological spaces. The relation of similarity of soft topological spaces is also introduced and examined. The soft topologies
T
1
and
T
2
on
X
are called similar, if the families
T
1
and
T
2
are mutually coinitial. We study some basic properties of similar soft topological spaces: we check whether the family of all such spaces forms a lattice, we examine the relationship between similarity and being homeomorphic and consider the similarity of
e
-parameterized topologies.
•The conditions are investigated under which the upper Vietoris topology coincides with the Scott topology on K(X).•For a well-filtered space X having a first-countable Smyth power space, the upper ...Vietoris topology and the Scott topology on (X) coincide.•For a first-countable T0 space in which the set of minimal elements of any compact saturated subset, its Smyth power space is first-countable.•For the Alexandroff double circle, which is first-countable, its Smyth power space is not first-countable.
For a T0 space X, let K(X) be the poset of all non-empty compact saturated sets of X with the reverse inclusion order. The space X is said to have property Q if for any K1,K2∈K(X), K1≪K2 in K(X) iff K2⊆intK1. In this paper, we give several connections among the well-filteredness of X, the sobriety of X, the local compactness of X, the core compactness of X, the property Q of X, the coincidence of the upper Vietoris topology and Scott topology on K(X), and the continuity of x↦↑x:X⟶ΣK(X) (where ΣK(X) is the Scott space of K(X)). It is shown that for a well-filtered space X for which its Smyth power space PS(X) is first-countable, the following three properties are equivalent: the local compactness of X, the core compactness of X and the continuity of K(X). It is also proved that for a first-countable T0 space X in which the set of minimal elements of K is countable for any compact saturated subset K of X, the Smyth power space PS(X) is first-countable. For the Alexandroff double circle Y, which is Hausdorff and first-countable, we show that its Smyth power space PS(Y) is not first-countable.
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