Local compactness in approach spaces. II.
Local compactness in bitopological hyperspace
Local compactness in bitopological spaces
Local connectedness and connected open functions.
Local connectedness, connectedness im kleinen, and another properties of hyperspaces of spaces
Local connectivity, open homogeneity and hyperspaces.
In the first part of the paper behavior of conditions related to local connectivity at a point is discussed if the space is transformed under a mapping that is interior or open at the considered point of the domain. The second part of the paper deals with metric locally connected continua. They are characterized as continua for which the hyperspace of their nonempty closed subjects is homogeneous with respect to open mappings. A similar characterization for the hyperspace of subcontinua remains...
Local expansions, derivatives, and fixed points
Local homeomorphisms [Book]
Local paracompactness
Local/global uniform approximation of real-valued continuous functions
For a Tychonoff space , is the lattice-ordered group (-group) of real-valued continuous functions on , and is the sub--group of bounded functions. A property that might have is (AP) whenever is a divisible sub--group of , containing the constant function 1, and separating points from closed sets in , then any function in can be approximated uniformly over by functions which are locally in . The vector lattice version of the Stone-Weierstrass Theorem is more-or-less equivalent...
Locally compact F-spaces, sub-stonean spaces and quotients of locally compact groups.
Locally compact linearly Lindelöf spaces
There is a locally compact Hausdorff space which is linearly Lindelöf and not Lindelöf. This answers a question of Arhangel'skii and Buzyakova.
Locally compact perfectly normal spaces may all be paracompact
We work towards establishing that if it is consistent that there is a supercompact cardinal then it is consistent that every locally compact perfectly normal space is paracompact. At a crucial step we use some still unpublished results announced by Todorcevic. Modulo this and the large cardinal, this answers a question of S. Watson. Modulo these same unpublished results, we also show that if it is consistent that there is a supercompact cardinal, it is consistent that every locally compact space...
Locally compact spaces whose Alexandroff one-point compactifications are perfect
Locally connected images of ordered compacta
Locally constant functions
Let X be a compact Hausdorff space and M a metric space. is the set of f ∈ C(X,M) such that there is a dense set of points x ∈ X with f constant on some neighborhood of x. We describe some general classes of X for which is all of C(X,M). These include βℕ, any nowhere separable LOTS, and any X such that forcing with the open subsets of X does not add reals. In the case where M is a Banach space, we discuss the properties of as a normed linear space. We also build three first countable Eberlein...
Locally equiconnected spaces and absolute neighborhood retracts
Locally fine uniformities and normal covers
Locally nearly paracompact spaces.
Locally nice spaces under Martin's axiom