Dimension and universality on frames

On sheaves of Abelian groups and universality

“…This method can be used for the construction of universal objects in different categories. Such categories are, for example, topological spaces (with different dimension invariants)(see [3], Chapter 3 of [9]), separable metric spaces (see Chapter 9 of [9], [10], [12], [13], [15]), mappings (see [8], Chapter 6 of [9], [10], [11]), topological groups ( [11], [14], [17]), G-spaces (see Chapter 7 of [9], [10], [11], [17], [18]) and frames (see [2], [4], [5], [6], [16]).…”

Μελέτη Της Θεωρίας Διαστάσεων Στην Περιοχή Των Τοπολογικών Χώρων Και Των Δικτυωτών

“…Stic ergasÐec [27] kai [55] eÐqe perigrafeÐ mÐa mèjodoc kataskeu c periektik¸n frames gia mÐa sullog L mh ken¸n kai xènwn metaxÔ touc frames, me stìqo thn apìdeixh Ôparxhc kajolik¸n stoiqeÐwn se kpoiec klseic frames, ìpwc gia pardeigma, sthn klsh ìlwn twn frames, kajèna apì ta opoÐa èqei broc mikrìtero Ðso tou τ .…”

“…H apeikìnish θ[L] kaleÐtai ∧-apeikìnish (gia peperasmèna inf imum) sth B L . (Genik, ìpwc diapist¸netai sthn ergasÐa [55], aut h apeikìnish den eÐnai monos manta orismènh. )…”

“…(Genik, ìpwc diapist¸netai sthn ergasÐa [55], h apeikìnish ϕ 0 den eÐnai monos manta orismènh.) Aut h epèktash kaleÐtai gn sia an gia kje L ∈ L kai gia kje t ∈ F, èqoume…”

“…Wstìso, to parapnw prìblhma kajolikìthtac apoteleÐ exÐsou shmantikì keflaio kai sth JewrÐa twn Frames, to opoÐo èqei anaptuqjeÐ mìlic th teleutaÐa dekaetÐa. Oi ergasÐec [27], [32], [42], [55], [56] kai [61] apoteloÔn thn arq enìc tètoiou kefalaÐou. ParallhlÐzontac ton orismì tou kajolikoÔ q¸rou, gia mÐa dojeÐsa klsh frames èna stoiqeÐo T aut c thc klshc kaleÐtai kajolikì (universal ) an uprqei frame-omomorfismìc kje stajeroÔ stoiqeÐou L aut c thc klshc epÐ tou T.…”