The search session has expired. Please query the service again.
Displaying 181 –
200 of
1531
We prove that a cosmic space (= a Tychonoff space with a countable network) is analytic if it is an image of a -analytic space under a measurable mapping. We also obtain characterizations of analyticity and -compactness in cosmic spaces in terms of metrizable continuous images. As an application, we show that if is a separable metrizable space and is its dense subspace then the space of restricted continuous functions is analytic iff it is a -space iff is -compact.
Several remarks on the properties of approximation by points (AP) and weak approximation by points (WAP) are presented. We look in particular at their behavior in product and at their relationships with radiality, pseudoradiality and related concepts. For instance, relevant facts are:
(a) There is in ZFC a product of a countable WAP space with a convergent sequence which fails to be WAP.
(b) over -compact space is AP. Therefore AP does not imply even pseudoradiality in function spaces, while...
The definitions of AP and WAP were originated in categorical topology by A. Pultr and A. Tozzi, Equationally closed subframes and representation of quotient spaces, Cahiers Topologie Géom. Différentielle Catég. 34 (1993), no. 3, 167-183. In general, we have the implications: , where is defined as the property that every compact subset is closed and is defined as the property that every convergent sequence has at most one limit. And a space is called submaximal if every dense subset is open....
We characterize Peano continua using Bing-Krasinkiewicz-Lelek maps. Also we deal with some topics on Whitney preserving maps.
We continue the study of topological properties of the group Homeo(X) of all homeomorphisms of a Cantor set X with respect to the uniform topology τ, which was started by Bezuglyi, Dooley, Kwiatkowski and Medynets. We prove that the set of periodic homeomorphisms is τ-dense in Homeo(X) and deduce from this result that the topological group (Homeo(X),τ) has the Rokhlin property, i.e., there exists a homeomorphism whose conjugacy class is τ-dense in Homeo(X). We also show that for any homeomorphism...
In this paper we discuss asymmetric length structures and asymmetric metric spaces. A length structure induces a (semi)distance function; by using the total variation formula, a (semi)distance function induces a length. In the first part we identify a topology in the set of paths that best describes when the above operations are idempotent. As a typical application, we consider the length of paths defined by a Finslerian functional in Calculus of Variations. In the second part we generalize the...
A nonzero -module is atomic if for each two nonzero elements in , both cyclic submodules and have nonzero isomorphic submodules. In this article it is shown that for an infinite -space , the factor rings and have no atomic ideals. This fact generalizes a result published in paper by A. Mozaffarikhah, E. Momtahan, A. R. Olfati and S. Safaeeyan (2020), which says that for an infinite set , the factor ring has no atomic ideal. Another result is that for each infinite -space , the...
Currently displaying 181 –
200 of
1531