We give some necessary and sufficient conditions for the character of spaces to be preserved under closed maps. Introduction. Recall the following result due to K. Morita and S. Hanai [11] or A. H. Stone [14]: Let Y be the image of a metric space X under a closed map/. Then Y is first countable (or metrizable) if and only if every boundary df~x(y) of the point-inverse/"'^) is compact. E. Michae...

In this note linearly ordered topological spaces (abbreviated LOTS) with a point-countable base are examined. It is shown that a LOTS is quasi-developable if and only if it has a <r-point-finite base and a LOTS with a point-countable base is paracompact. An example of a LOTS with a point-countable base that does not have a <r-point-finite base is given. Conditions are given for the metrizabilit...

Programming languages with countable nondeterministic choice are computationally interesting since countable nondeterminism arises when modeling fairness for concurrent systems. Because countable choice introduces non-continuous behaviour, it is well-known that developing semantic models for programming languages with countable nondeterminism is challenging. We present a step-indexed logical re...

We prove a strong convergence result for a sequence generated by Halpern's type iteration for approximating a common fixed point of a countable family of quasi-Lipschitzian mappings in a real Hilbert space. Consequently, we apply our results to the problem of finding a common fixed point of asymptotically nonexpansive mappings, an equilibrium problem, and a variational inequality problem for co...

In this paper, we establish the relationships between spaces with a compact-countable weak-base and spaces with various compact-countable networks, and give two mapping theorems on spaces with compact-countable weakbases. Weak-bases and g-first countable spaces were introduced by A.V.Arhangel’skii [1]. Spaces with a point-countable weak-base were discussed in [5,6], and spaces with a locally co...

Abstract We show that the image of a subshift X under various injective morphisms symbolic algebraic varieties over monoid universes with variety alphabets is finite type, respectively sofic subshift, if and only so . Similarly, let G be countable A , B Artinian modules ring. prove for every closed submodule $\Sigma \subset A^G$ -equivariant uniformly continuous module homomorphism $\tau \colon...

We present constructions of countable two-dimensional subshifts of finite type (SFTs) with interesting properties. Our main focus is on properties of the topological derivatives and subpattern posets of these objects. We present a countable SFT whose iterated derivatives are maximally complex from the computational point of view, constructions of countable SFTs with high CantorBendixson ranks, ...

In the theory of generalized metric spaces, the notion of knetworks has played an important role. Every locally separable metric space or CW-complex, more generally, every space dominated by locally separable metric spaces has a star-countable k-network. Every LaSnev space, as well as, every space dominated by LaSnev spaces has a a-compact-finite knetwork. We recall that every space has a compa...

We investigate the relation between intermediate predicate logics based on countable linear Kripke frames with constant domains and Gödel logics. We show that for any such Kripke frame there is a Gödel logic which coincides with the logic defined by this Kripke frame on constant domains and vice versa. This allows us to transfer several recent results on Gödel logics to logics based on countabl...