Notice that Hausdorffness of the topology induced by the uniformity guarantees the uniqueness of limit of a sequence in uniform spaces.
We have marked the very corporate-like environment we work in – all straight lines, uniform spaces, impenetrable concrete, unbending steel – with signs of alternative voices, thoughts-in-the-making and issues up for debate.
Conceived by Mr. Childs as a series of identical floors on the first four stories that frame a vast glass atrium overlooking Columbus Circle and 59th Street, the mall's uniform spaces -- clad in expensive-looking gray granite and glass -- are a vision of suburban ennui.
Distances in uniform spaces were given by Vályi [14].
For example, metric spaces, fuzzy metric spaces, and uniform spaces.
It is possible to generalise his theory to uniform spaces, but for some applications this is clearly not sufficient: for instance, quotient spaces of uniform spaces need not be uniform spaces, a fact that bars direct applicability to fields such as algebraic topology.
For details, see, e.g., [7] in normed spaces; [8 11] in metric spaces; [12] in uniform spaces; and [13 22] in quasi-gauge, cone uniform and uniform spaces.
Now, we recall some relevant definitions and properties from the foundation of uniform spaces.
Therefore, all the results proved previously for uniform spaces also apply to locally convex spaces.
Moreover, in uniform spaces, the J -families on these spaces generalize distances of Vályi [30].
For more details about uniform spaces, we refer the reader to Kelley [25].
