Storrer introduced the epimorphic hull of a commutative semiprime ring R and showed that it is (up to isomorphism) the unique essential epic von Neumann regular extension of R. In the case when R = C(X) with X a Tychonoff space, we show that the embedding induced by a dense subspace of X is always essential. This simplifies the search for spaces whose epimorphic hull is a full ring of continuou...

Cardinalities and lattice structures which are attainable by semilattices of ordered compactifications of completely regular ordered spaces are examined. Visliseni and Flachsmeyer have shown that every infinite cardinal is attainable as the cardinality of a semilattice of compactifications of a Tychonoff space. Among the finite cardinals, however, only the Bell numbers are attainable as cardina...

We explore almost-normality in Isbell-Mr\'owka spaces and some related concepts. use forcing to provide an example of almost-normal not normal almost disjoint family, the concept semi-normality spaces, define strongly $(\aleph_0, <\mathfrak c)$-separated families prove generic existence completely separable c)$-almost assuming $\mathfrak s=\mathfrak c$ b=\mathfrak c$. also a Tychonoff pseudocom...

In this paper, we have proved results similar to Tychonoff's Theorem on embedding a space of functions with the topology pointwise convergence into Tychonoff product topological spaces, but applied function C(X,Y) all continuous from X uniform Y family subsets and (weak) set-open topology. We also investigated following question: how is related algebraic structures (such as groups, rings vector...

According to the celebrated theorem of Comfort and Ross (1966), the product of an arbitrary family of pseudocompact topological groups is pseudocompact. We present an overview of several important generalizations of this result, both of “absolute” and “relative” nature. One of them is the preservation of functional boundedness for subsets of topological groups. Also we consider close notions of...

The concept of ‘topological right transversal’ is introduced to study right transversals in topological groups. Given any right quasigroup S with a Tychonoff topology T , it is proved that there exists a Hausdorff topological group in which S can be embedded algebraically and topologically as a right transversal of a subgroup (not necessarily closed). It is also proved that if a topological rig...

It is the purpose of this paper to go somewhat deeper into the structure of fuzzy topological spaces. In doing so we found we had to alter the definition of a fuzzy topology used up to now. We shall also introduce two functors 3 and i which will allow us to see more clearly the connection between fuzzy topological spaces and topological spaces. Finally we shall introduce the concept of fuzzy co...

A topological space X is Baire if the intersection of any sequence open dense subsets in X. Let $$C_p(X,[0,1])$$ denote all continuous [0, 1]-valued functions on a Tychonoff with topology pointwise convergence. In this paper, we have obtained characterization for function to be separable closed which are $$C^*$$ -embedded. particular, holds normal spaces and, hence, metrizable spaces. Moreover,...

Constructions related to products of maximal linked systems (MLSs) and MLSs on the product widely understood measurable spaces are considered (these defined as sets equipped with \(\pi\)-systems their subsets; a \(\pi\)-system is family closed respect finite intersections). We compare families initial product. Separately, we consider case ultrafilters. Equipping set-products topologies, use box...

In this paper, we provide several Arzelà–Ascoli-type results on the space of all continuous functions from a Tychonoff X into fuzzy sets Rn, (FUSCB(Rn),Hend), which are upper semi-continuous and have bounded support endowed with endograph metric. Namely, obtain positive when is considered to be kr-space C(X,(FUSCB(Rn),Hend)) compact open topology, as well assume that pseudocompact equipped unif...