Locally compact space and continuity

Locally Non-compact Spaces and Continuity Principles

We give a constructive proof that Baire space embeds in any inhabited locally non-compact complete separable metric space, X, in such a way that every sequentially continuous function from Baire space to Z extends to a function from X to R. As an application, we show that, in the presence of certain choice and continuity principles, the statement “all functions from X to R is continuous” is fal...

Uniform continuity over locally compact quantum groups

We define, for a locally compact quantum group G in the sense of Kustermans– Vaes, the space of LUC (G) of left uniformly continuous elements in L∞(G). This definition covers both the usual left uniformly continuous functions on a locally compact group and Granirer’s uniformly continuous functionals on the Fourier algebra. We show that LUC (G) is an operator system containing the C∗-algebra C0(...

TOPOLOGICALLY STATIONARY LOCALLY COMPACT SEMIGROUP AND AMENABILITY

In this paper, we investigate the concept of topological stationary for locally compact semigroups. In [4], T. Mitchell proved that a semigroup S is right stationary if and only if m(S) has a left Invariant mean. In this case, the set of values ?(f) where ? runs over all left invariant means on m(S) coincides with the set of constants in the weak* closed convex hull of right translates of f. Th...

P-Amenable Locally Compact Hypergroups

CONTINUITY IN FUNDAMENTAL LOCALLY MULTIPLICATIVE TOPOLOGICAL ALGEBRAS

Abstract. In this paper, we first derive specific results concerning the continuity and upper semi-continuity of the spectral radius and spectrum functions on fundamental locally multiplicative topological algebras. We continue our investigation by further determining the automatic continuity of linear mappings and homomorphisms in these algebras.