The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
Displaying 21 –
40 of
347
A condensation is a one-to-one continuous mapping onto. It is shown that the space of real-valued continuous functions on in the topology of pointwise convergence very often cannot be condensed onto a compact Hausdorff space. In particular, this is so for any non-metrizable Eberlein compactum (Theorem 19). However, there exists a non-metrizable compactum such that condenses onto a metrizable compactum (Theorem 10). Several curious open problems are formulated.
Arhangel’skiǐ proved that if and are completely regular spaces such that and are linearly homeomorphic, then is pseudocompact if and only if is pseudocompact. In addition he proved the same result for compactness, -compactness and realcompactness. In this paper we prove that if is a continuous linear surjection, then is pseudocompact provided is and if is a continuous linear injection, then is pseudocompact provided is. We also give examples that both statements do not hold...
A polyadic space is a Hausdorff continuous image of some power of the one-point compactification of a discrete space. We prove a Ramsey-like property for polyadic spaces which for Boolean spaces can be stated as follows: every uncountable clopen collection contains an uncountable subcollection which is either linked or disjoint. One corollary is that is not a universal preimage for uniform Eberlein compact spaces of weight at most κ, thus answering a question of Y. Benyamini, M. Rudin and M. Wage....
M. Radulescu proved the following result: Let be a compact Hausdorff topological space and a supra-additive and supra-multiplicative operator. Then is linear and multiplicative. We generalize this result to arbitrary topological spaces.
We get the following result. A topological space is strongly paracompact if and only if for any monotone increasing open cover of it there exists a star-finite open refinement. We positively answer a question of the strongly paracompact property.
A DC-space (or space of dense constancies) is a Tychonoff space such that for each there is a family of open sets , the union of which is dense in , such that , restricted to each , is constant. A number of characterizations of DC-spaces are given, which lead to an algebraic generalization of the concept, which, in turn, permits analysis of DC-spaces in the language of archimedean -algebras. One is led naturally to the notion of an almost DC-space (in which the densely constant functions...
Currently displaying 21 –
40 of
347