In 1961, J. G. Ceder [3] introduced and studied classes of topological spaces called Mi-spaces (i = 1, 2, 3) and established that metrizable ⇒ M1 ⇒ M2 ⇒ M3. He then asked whether these implications are reversible. Gruenhage [5] and Junnila [8] independently showed that M3 ⇒ M2. In this paper, we investigate the M1-and M3-properties in the setting of ordered topological spaces. Among other results, we show that if (X, T, ≤) is an M1 ordered topological C-and I-space then the bitopological space
Abstract:We show that the image of a q-hyperconvex quasi-metric space under a retraction is q-hyperconvex. Furthermore, we establish that quasi-tightness and quasi-essentiality of an extension of a T 0 -quasi-metric space are equivalent.
The investigation of metric trees began with J. Tits in 1977. Recently we studied a more general notion of quasi-metric tree. In the current article we prove, among other facts, that the q -hyperconvex hull of a q -hyperconvex T0 -quasi-metric tree is itself a T0 -quasi-metric tree. This is achieved without using the four-point property, a geometric concept used by Aksoy and Maurizi to show that every complete metric tree is hyperconvex.
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