Unified characterization of exponential objects in TOP, PRTOP and PARATOP
More on strongly sequential spaces
Strongly sequential spaces were introduced and studied to solve a problem of Tanaka concerning the product of sequential topologies. In this paper, further properties of strongly sequential spaces are investigated.
Strongly sequential spaces
The problem of Y. Tanaka [10] of characterizing the topologies whose products with each first-countable space are sequential, is solved. The spaces that answer the problem are called strongly sequential spaces in analogy to strongly Fréchet spaces.
Productively Fréchet spaces
We solve the long standing problem of characterizing the class of strongly Fréchet spaces whose product with every strongly Fréchet space is also Fréchet.
Closure spaces and characterizations of filters in terms of their Stone images
Fréchet, strongly Fréchet, productively Fréchet, weakly bisequential and bisequential filters (i.e., neighborhood filters in spaces of the same name) are characterized in a unified manner in terms of their images in the Stone space of ultrafilters. These characterizations involve closure structures on the set of ultrafilters. The case of productively Fréchet filters answers a question of S. Dolecki and turns out to be the only one involving a non topological closure structure.
Strongly sequential spaces.
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